Sum of roots (Vieta's)

Find the sum of all roots directly from the coefficients using Vieta's formulas — no need to solve!

p(x) =

Vieta's formulas

For ax²+bx+c = 0: Sum of roots = −b/a. Product of roots = c/a.

For x²−5x+6: sum = −(−5)/1 = 5. (Roots are 2 and 3, and 2+3 = 5 ✓)

Higher degrees

For ax³+bx²+cx+d: sum of roots = −b/a. Sum of products of pairs = c/a. Product of all roots = −d/a.

Popular quadratic equations
Related calculators