How this calculation works
Expanding a(x−r₁)(x−r₂) gives the same coefficients and explains both identities.
THE FORMULA
r₁ + r₂ = −b/a, r₁r₂ = c/aA worked example
For 2x²−7x+3, the root sum is 7/2 and the product is 3/2.
Good to know
The identities apply to complex roots too.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Apply Viète’s identities directly to the coefficients.
The primary result is labeled “Sum of roots”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The identities apply to complex roots too.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For 2x²−7x+3, the root sum is 7/2 and the product is 3/2.
Which rule does this calculator apply?
r₁ + r₂ = −b/a, r₁r₂ = c/a