Polynomials — Formula Sheet

Expressions like 1/x + 1, √x + 2 are NOT polynomials because they contain negative or fractional powers

For quadratic ax² + bx + c with zeros α, β

Sum = -b/a, Product = c/a

A real number k is a zero of polynomial p(x) if p(k) = 0.

For example, if p(x) = x² - 3x - 4, then p(4) = 16 - 12 - 4 = 0, so 4 is a zero.

For quadratic polynomial ax² + bx + c with zeroes α and β

Sum of zeroes: α + β = -b/a.

Product of zeroes

αβ = c/a.

For cubic polynomial ax³ + bx² + cx + d with zeroes α, β, γ

Sum of zeroes: α + β + γ = -b/a.

Sum of products taken two at a time

αβ + βγ + γα = c/a.