Question

Find the zeroes of the following polynomial by factorization method: $2x^2+\frac{7}{2}x+\frac{3}{4}$.

Answer 1

Factorise the given polynomial to find its zeroes

Given $2x^2+\frac{7}{2}x+\frac{3}{4}$

By splitting the middle term, we can write that

$2x^2+\frac{7}{2}x+\frac{3}{4}=2x^2+\frac{6}{2}x+\frac{1}{2}x+\frac{3}{4}$

Next, take the common terms out.

$2x^2+\frac{7}{2}x+\frac{3}{4}=2x(x+\frac{3}{2})+\frac{1}{2}(x+\frac{3}{2})$

$=\left(2x+\frac{1}{2}\right)\left(x+\frac{3}{2}\right)$

The zeroes can be found as

$\left(2x+\frac{1}{2}\right)\left(x+\frac{3}{2}\right)=0$

$\left(2x+\frac{1}{2}\right)=0$ or $\left(x+\frac{3}{2}\right)=0$

$x=-\frac{1}{4}$ or $x=-\frac{3}{2}$

Hence, the zeroes of the polynomial are $-\frac{1}{4},-\frac{3}{2}$.