Find the zeroes of the quadratic polynomial. p(x) = x^2 – 4

Question

Find the zeroes of the quadratic polynomial. Find the sum and product of the zeroes and verify relationship to the coefficients of terms in the polynomial.

p(x) = x² – 4

Answer 1

Given polynomial p(x) = x² – 4 

We have, x² – 4 = (x – 2) (x + 2) 

So, the value of x² – 4 is zero 

when x – 2 = 0 or x + 2 = 0 

i.e., x = 2 or x = – 2 

So the zeroes of x² – 4 are 2 and – 2 

∴ Sum of the zeroes = 2 + (- 2) = 0

\( =-\frac{Coefficient\,of\,x}{Coefficient\,of\,x^2}= \frac{-0}{1}=1\)

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

\( =\frac{Consatnt\,term}{Coefficient\,of\,x^2}=\frac{-4}{1} =-4\)