Question

Find the zeroes of the polynomial $x^2+4\sqrt{3}x-15=0$ by factorization method.

Answer 1

Step 1: Form the equation

The given polynomial is $x^2+4\sqrt{3}x-15=0$

We know that the zeroes of a polynomial are evaluated by equating it with zero.

$\therefore p\left(x\right)=0$

$\Rightarrow x^2+4\sqrt{3}x-15=0$

Step 2: Solve to find the zeroes

$x^2+4\sqrt{3}x-15=0$

$\Rightarrow$ $x^2+5\sqrt{3}x-\sqrt{3}x-15=0$

$\Rightarrow$$x\left(x+5\sqrt{3}\right)-\sqrt{3}\left(x+5\sqrt{3}\right)=0$

$\Rightarrow$ $\left(x+5\sqrt{3}\right)\left(x-\sqrt{3}\right)=0$

$\Rightarrow$ $x=-5\sqrt{3},\sqrt{3}$

Hence, the zeroes of this polynomial are $-5\sqrt{3}$ and $\sqrt{3}$.