Stage 11 · Quadratic Equations

11.5.1 The Pattern in the Sum and Product of the Roots

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

Point 1 of 4

11.5.1 The Pattern in the Sum and Product of the Roots

Core idea

Add the two branches of the quadratic formula, then multiply them, and you'll be delighted to find the sum of the roots is −b/a and their product is c/a.

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.
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