Question

Find the zeros of the quadratic polynomials x² + 7x + 12 and verify the relationship between the zeros and the coefficients.

Answer 1

Let f(x) = x² + 7x + 12

f(x) = x² + 4x + 3x + 12

f(x) = x(x+4) + 3(x+4)

f(x) = (x+4)(x+3)

To find the zeroes, set f(x) = 0, then

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

x = −4 or x = −3

Again,

Sum of zeroes = (-4 – 3) = -7 = -7/1

= -b/a

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

Product of zeroes = 12 = 12/1

= c/a

= Constant term / Coefficient of x²