Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: x 2 + 2x – 8

Philoid · Accepted Answer

Let f(x) = x² + 2x - 8

Put f(x) = 0

x² + 2x - 8 = 0

x² + 2x - 4x - 12 = 0

x(x + 2) – 4 (x + 2) = 0

(2 + x) (x - 4) = 0

∴ x = 4 or x = -2

Now, sum of zeroes = -2 + 4 = 2 =

Product of zeroes = (4) × (-2)

Hence, relationship verified.