Question

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

t² – 15

Answer 1

Given polynomial is t² – 15. 

We have, t² – 15 = (t – √15 ) (t + √15) 

The value of t² – 15 is 0, 

when the value of (t – √15 ) (t + √15) = 0, i.e., 

when t – √15 = 0 or t + √15 = 0, i.e., 

when t = √15 (or) t = -√15 

∴ The zeroes of t² – 15 are √15 and -√15. 

Therefore, sum of the zeroes = √15 + (-√15) = 0

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

And product of the zeroes √15 × (-√15) = -15

\(=\frac{Constant\,term}{Coefficient\,of\,t^2}=\frac{-15}{1}=-15\)