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 + 7x + 12

Philoid · Accepted Answer

Let f(x) = x² + 7x + 12

Put f(x) = 0

x² + 7x + 12 = 0

x² + 4x + 3x + 12 = 0

3(x + 4) + x(x + 4) = 0

(3 + x) (x + 4) = 0

∴ x = -4 or x = -3

Now,

sum of zeroes = -3 + (-4) = -7=

Product of zeroes = (-3) × (-4)

Hence, relationship verified.