Yes, there is just a limited amount of polynomials for which we can find the exact, i.e. algebraic roots by some general formula (like it’s possible for quadratic polynomials).
- 1 Can a polynomial have no solution?
- 2 How many solutions do polynomials have?
- 3 How do you tell if a polynomial has no real solutions?
- 4 Can you solve any polynomial?
- 5 Which equations have no solution?
- 6 Do all quadratic equations have solutions?
- 7 What equation has no solution?
- 8 What is an example of no solution?
- 9 What does no real solutions mean?
- 10 How do you find all solutions?
- 11 How do you find possible solutions?
- 12 How are polynomial equations solved?
- 13 How do you find all real solutions?
- 14 How do you solve polynomial fractions?
- 15 How do you solve polynomial operations?
- 16 How do you know if there is no solution or infinite solutions?
- 17 How many solutions are there?
- 18 How many solutions are there in a quadratic equation?
- 19 Which inequality has no solution?
- 20 How do you know if a quadratic equation has real solutions?
- 21 Do all quadratic equations have 2 solutions?
- 22 What are infinitely many solutions?
- 23 What are infinite solutions examples?
- 24 Do parabolas have solutions?
- 25 What are irrational solutions?
- 26 How do you find complex solutions?
- 27 How do you know if a solution is all real numbers?
- 28 Which are not polynomials?
- 29 Does every problem have a solution?
- 30 What does all real solutions mean?
- 31 How do you find all real solutions by factoring?
- 32 What is the best solution in decision making?
- 33 How do you solve adding and subtracting polynomials?
- 34 How do you solve a polynomial in standard form?
- 35 What are the steps in solving problems involving polynomials and polynomial equations?
- 36 Can polynomials be fractions?
- 37 What are the rules of polynomials?
- 38 Why are fractions not polynomials?
- 39 Which operation is not performed in polynomial?
- 40 Can we consider polynomials to be algebraic expression?
- 41 Are all polynomials algebraic expressions?
- 42 Is no solution dependent or independent?
- 43 How do you know if a matrix has infinite solutions?
- 44 What is the condition for no solution?
- 45 What is an example of one solution?
- 46 Can a polynomial inequality have no solution?
- 47 How many solutions does an inequality have?
- 48 Why can an inequality have no solution?
- 49 How do you find the number of real solutions without solving?
- 50 How do you tell if a quadratic has no solution?
-
51
Why do quadratics have two solutions?
-
51.1
Related Posts
- 51.1.1 Do absolute value equations always have two solutions?
- 51.1.2 Why are quintic unsolvable?
- 51.1.3 Do all equations have variables?
- 51.1.4 Do acids dissolve in water to form aqueous solutions?
- 51.1.5 Did rule like dissolve like hold true for all solutions?
- 51.1.6 Do bases turn phenolphthalein pink?
-
51.1
Related Posts
Can a polynomial have no solution?
In mathematics, the Abel–Ruffini theorem (also known as Abel’s impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates.
How many solutions do polynomials have?
A polynomial equation of degree n has at most n solutions. A polynomial equation of degree n has exactly n solutions, if you count them with multiplicity. Perhaps a bit surprisingly, the commutativity of fields is essential for this: The equation x2+1=0 has infinitely many solutions.
How do you tell if a polynomial has no real solutions?
If the discriminant is positive, there are exactly 2 real solutions. If the discriminant is zero, there is exactly one real solution (a repeated root). If the discriminant is negative, there are exactly 2 complex solutions (they are complex conjugates), with no real solution.
Can you solve any polynomial?
https://www.youtube.com/watch?v=g7_llQnLepA
Which equations have no solution?
A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.
Do all quadratic equations have solutions?
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.
What equation has no solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
What is an example of no solution?
As an example, consider 3x + 5 = 3x – 5. This equation has no solution. There is no value that will ever satisfy this type of equation.
What does no real solutions mean?
“No solution” means that there is no value, not even 0, which would satisfy the equation. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.
How do you find all solutions?
https://www.youtube.com/watch?v=ZroxCI62p5k
How do you find possible solutions?
https://www.youtube.com/watch?v=1GELhpaRt6g
How are polynomial equations solved?
To solve a linear polynomial, set the equation to equal zero, then isolate and solve for the variable. A linear polynomial will have only one answer. If you need to solve a quadratic polynomial, write the equation in order of the highest degree to the lowest, then set the equation to equal zero.
How do you find all real solutions?
https://www.youtube.com/watch?v=tRrPfxR5h-w
How do you solve polynomial fractions?
When adding and/or subtracting polynomial fractions, first get common denominators, then add and/or subtract the numerators together. Finally, simplify. To solve a complex fraction, first find the common denominator for the entire fraction. Then change each term’s denominator to this common denominator.
How do you solve polynomial operations?
https://www.youtube.com/watch?v=aWuLXONc-VM
How do you know if there is no solution or infinite solutions?
We can identify which case it is by looking at our results. If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
How many solutions are there?
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
How many solutions are there in a quadratic equation?
A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.
Which inequality has no solution?
If an inequality has no real solution, this means that there are no numbers that can be substituted into the inequality to make the statement true. If an inequality has all real numbers as the solution, this means that every real number can be substituted into the inequality to make a true statement.
How do you know if a quadratic equation has real solutions?
- A positive discriminant indicates that the quadratic has two distinct real number solutions.
- A discriminant of zero indicates that the quadratic has a repeated real number solution.
Do all quadratic equations have 2 solutions?
A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. There are several methods you can use to solve a quadratic equation: Factoring.
What are infinitely many solutions?
Equations with an infinite number of solutions
If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.
What are infinite solutions examples?
An infinite solution has both sides equal. For example, 6x + 2y – 8 = 12x +4y – 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution.
Do parabolas have solutions?
If the parabola and the line touch at a single point, then there is one solution that is true for both equations. If the graphs of the equations do not intersect, then there are no solutions that are true for both equations.
What are irrational solutions?
Irrational solutions – An irrational number is a number that cannot be written as a fraction. In these cases, the equation does not have a perfect square, but the solutions can be found by taking the square root and rounding.
How do you find complex solutions?
https://www.youtube.com/watch?v=i8KSC5J6_Wo
How do you know if a solution is all real numbers?
1. If solving a linear equation leads to a true statement such as 0 = 0, the equation is an identity. Its solution set is {all real numbers}.
Which are not polynomials?
Polynomials cannot contain fractional exponents. Terms containing fractional exponents (such as 3x+2y1/2-1) are not considered polynomials. Polynomials cannot contain radicals. For example, 2y2 +√3x + 4 is not a polynomial.
Does every problem have a solution?
There is always a solution
While they may not have a “correct” answer, they do have a “best” answer and you can do your best to find out what that is. If you don’t believe every problem can be solved, you’re not going to try very hard to solve it, are you?
What does all real solutions mean?
If the value of the discriminant is positive, there are two real solutions for x, meaning the graph of the solution has two distinct x-intercepts. If the value of the discriminant is zero, there is one real solution for x, meaning the graph of the solution has one x-intercept.
How do you find all real solutions by factoring?
- Move all terms to one side of the equation, usually the left, using addition or subtraction.
- Factor the equation completely.
- Set each factor equal to zero, and solve.
- List each solution from Step 3 as a solution to the original equation.
What is the best solution in decision making?
- Don’t let stress get the better of you. …
- Give yourself some time (if possible). …
- Weigh the pros and cons. …
- Think about your goals and values. …
- Consider all the possibilities. …
- Talk it out. …
- Keep a diary. …
- Plan how you’ll tell others.
How do you solve adding and subtracting polynomials?
https://www.youtube.com/watch?v=0aJBtUOXpsk
How do you solve a polynomial in standard form?
https://www.youtube.com/watch?v=53x8cIPf8X0
What are the steps in solving problems involving polynomials and polynomial equations?
https://www.youtube.com/watch?v=uuM1v8ujDAs
Can polynomials be fractions?
A polynomial can have fractions involving just the numbers in front of the variables (the coefficients), but not involving the variables.
What are the rules of polynomials?
In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
Why are fractions not polynomials?
Another rule of thumb is if there are any variables in the denominator of a fraction then the algebraic expression isn’t a polynomial. There are lots of radicals and fractions in this algebraic expression, but the denominators of the fractions are only numbers and the radicands of each radical are only a numbers.
Which operation is not performed in polynomial?
A polynomial is a mathematical expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, and multiplication.
Can we consider polynomials to be algebraic expression?
Polynomials are algebraic expressions that are created by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation. You can create a polynomial by adding or subtracting terms.
Are all polynomials algebraic expressions?
No, not all algebraic expressions are polynomials. But all polynomials are algebraic expressions. The difference is polynomials include only variables and coefficients with mathematical operations(+, -, ×) but algebraic expressions include irrational numbers in the powers as well.
Is no solution dependent or independent?
An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.
How do you know if a matrix has infinite solutions?
In simple words, when a system is consistent, and the number of variables is more than the number of nonzero rows in the RREF of the matrix, the matrix equation will have infinitely many solutions.
What is the condition for no solution?
If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. This type of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel and system of equations have no solution. Example. Find the value of x and y.
What is an example of one solution?
Linear Equations With one Solution
On solving we have 7x = 35 or x = 5. The above linear equation is only true if x = 5 and hence the given linear equation has only one solution i.e. x = 5. Example 2: Consider the equation 9(x – 1) – 35 = 8x + 37. On solving we have 9x – 9 – 35 = 8x + 37.
Can a polynomial inequality have no solution?
As with equalities, it’s possible for inequalities to have no solution.
How many solutions does an inequality have?
Typically an inequality has infinitely many solutions and the solution set is easily described using interval notation. The solution set of example 1 is the set of all x <= 7.
Why can an inequality have no solution?
Some inequalities do not have a solution. When two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded), then the system has no solution. This means that there is no coordinate point that makes both inequalities true.
How do you find the number of real solutions without solving?
https://www.youtube.com/watch?v=fmX165Lh5a4
How do you tell if a quadratic has no solution?
The first way to tell if a quadratic has no real solution is to look at the discriminant. If the discriminant is negative, then the quadratic equation has no real solution. The discriminant is the expression b2 – 4ac under the radical in the quadratic formula.
Why do quadratics have two solutions?
1 Answer. A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.