Vieta's formulas calculator for quadratic equations. Find the sum and product of roots, or relate roots to coefficients with x1 + x2 = -b/a and x1x2 = c/a.
Use this Vieta's formulas calculator for a quadratic equation to connect the roots x1 and x2 with the coefficients of ax2 + bx + c. It is useful for algebra practice, checking factorization, and understanding how the sum and product of roots relate to the original equation.
For a quadratic equation, Vieta's formulas give x1 + x2 = -b/a and x1x2 = c/a. This calculator lets you enter the two roots and immediately see those coefficient relationships.
Vieta's Formulas FAQ
What are Vieta's formulas for a quadratic equation?
For ax^2 + bx + c = 0 with roots x1 and x2, Vieta's formulas are x1 + x2 = -b/a and x1x2 = c/a.
What does this Vieta's formulas calculator do?
This calculator takes the two roots of a quadratic equation and returns the corresponding values of -b/a and c/a. That helps you connect the roots to the coefficients without expanding the polynomial by hand.
What are Vieta's formulas used for?
Vieta's formulas are used to relate the roots of a quadratic equation to its coefficients, check whether proposed roots are correct, build a quadratic from known roots, and support factorization and algebra simplification.
How do you use Vieta's theorem to find the sum and product of roots?
Add the two roots to get x1 + x2, which equals -b/a. Multiply the two roots to get x1x2, which equals c/a.
Can Vieta's formulas recover the original quadratic equation?
Only up to a scale factor unless a is known. From the roots alone, you can recover the monic form x^2 - (x1 + x2)x + x1x2 = 0, or the general family a(x - x1)(x - x2) = 0. A unique original quadratic requires the leading coefficient a.
How do Vieta's formulas relate to factorization?
If the roots are known, the quadratic can be written as a(x - x1)(x - x2). Expanding that form gives the same coefficient relationships as Vieta's formulas.
Example: if the roots are 2 and 3, what are -b/a and c/a?
If x1 = 2 and x2 = 3, then x1 + x2 = 5, so -b/a = 5. Their product is 2 × 3 = 6, so c/a = 6.
