Question

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

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

x² + 7x + 12

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)

= `(-7)/1`

= `(-("Coefficient of " x))/(("Cofficient of " x^2))` 

Product of zeroes = (– 4) (– 3)

= `12/1`

= `("Constant term")/(("Coefficient of " x^2))`