Find the zeroes of the quadratic polynomial. p(x) = x^2 + 2x + 1

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 + 2x + 1

Answer 1

Given polynomial p(x) = x² + 2x + 1 

We have x² + 2x + 1 = x² + x + x + 1 

= x(x + 1) + l(x + 1) 

= (x + 1) (x + 1) 

So, the value of x² + 2x + 1 is zero 

when x + 1 = 0 (or) x + 1 = 0, i.e., 

when x = – 1 or – 1 

So, the zeroes of x² + 2x + 1 are – 1 and – 1. 

∴ Sum of the zeroes = (-1) + (-1) = -2

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

And product of the zeroes = (-1) × (-1) = 1

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