Question

Find the zeros of the polynomial f(x) = x² + 7x + 12 and verify the relation between its zeroes and coefficients.

Answer 1

x² + 7x + 12 = 0 

⇒ x² + 4x + 3x + 12 = 0 

⇒ x(x+4) + 3(x+4) = 0 

⇒ (x+4) (x+3) = 0 

⇒ (x + 4) = 0 or (x + 3) = 0 

⇒ x = −4 or x = −3 

Sum of zeroes = −4 + (−3) = \(\frac{-7}1\) = \(\frac{-(coefficient\,of\,x)}{(coefficient\,of\,x^2)}\)

Product of zeroes = (−4) (−3) = \(\frac{12}1\) = \(\frac{constant\,term}{(coefficient\,of\,x^2)}\)