Question

Find the zeroes of the following polynomial by factorisation method: $5t^2+12t+7$.

Answer 1

Factorise the given polynomial to find the zeroes

Given polynomial, $5t^2+12t+7$

First, split the middle term.

$5t^2+12t+7=5t^2+5t+7t+7$

$=5t(t+1)+7(t+1)$ [ Taking common terms out ]

$=(t+1)(5t+7)$

The zeroes can be found as

$(t+1)(5t+7)=0$

$t+1=0$ or $5t+7=0$

$t=-1$ or $t=-\frac{7}{5}$

Hence, the zeroes of the polynomial are $-1$ and $-\frac{7}{5}$.