Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient. x^2 – 2x – 8

Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

x² – 2x – 8

Answer 1

Given polynomial is x² – 2x – 8 

We have x² – 2x – 8 = x² – 4x + 2x – 8 

= x(x – 4) + 2(x – 4) 

= (x – 4) (x + 2) 

So, the value of x² – 2x – 8 is zero 

when x – 4 = 0 or x + 2 = 0 i.e., 

when x = 4 or x = -2 

So, the zeroes of x² – 2x – 8 are 4 and -2.

Sum of the zeroes = 4 – 2 = 2 Coefficient of ,x - (-2)

= \(-\frac{coefficient\,of\,x}{coefficent\,of\,x^2} = \frac{-(-2)}{1}= 2\)

And product of the zeroes = 4 × (-2) = -8

= \(\frac{Constant\,term}{coefficient\,of\,x^2}=\frac{-8}{1}=-8 \)