Question

Find the zeroes of the following polynomial by factorisation method: $4x^2-3x-1$.

Answer 1

Factorise the given polynomial to find its zeroes

Given polynomial, $4x^2-3x-1$

First, split the middle term.

$4x^2-3x-1=4x^2-4x+1x-1$

$=4x(x-1)+1(x-1)$ [ Taking the common terms out ]

$=\left(x-1\right)\left(4x+1\right)$

The zeroes can be found as

$\left(x-1\right)\left(4x+1\right)=0$

$\left(x-1\right)=0$ or $\left(4x+1\right)=0$

$x=1$ or $x=-\frac{1}{4}$

Hence, the zeroes of the polynomial are $1$ and $-\frac{1}{4}$.