Question

Find the zeros of the quadratic polynomial f(x) = x² - 2x - 8 and verify and the relationship between the zeros and their coefficients.

Answer 1

f(x) = x² - 2x - 8

=>f(x) = x² - 4x + 2x - 8 

=>f(x) = x(x - 4) + 2(x - 4)]

=>f(x) = (x - 4) (x + 2)

Zeros of f(x) are given by f(x) = 0

=>x² - 2x - 8 = 0 =

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

=>x = 4 or x = - 2

So, a = 4 and b = −2

sum of zeros α + β

= 4 - 2 = 2