Stage 11 · Quadratic Equations

11.5.4 Building an Equation from Its Roots

11.5 The Relationship Between Roots and Coefficients (Vieta's Formulas)

Point 4 of 4

11.5.4 Building an Equation from Its Roots

Core idea

Given two roots, use Vieta's in reverse: take the sum and product as coefficients to write x²−(sum)x+(product)=0.

Module goal. Read off the sum and product of the two roots without solving, then work backwards to build an equation from its roots and evaluate symmetric expressions.
eastmath.com · 11.5 The Relationship Between Roots and Coefficients (Vieta's Formulas) · 11.5.4 Building an Equation from Its Roots