Question

Find the zeroes of the following polynomial:$5\sqrt{5}{x}^2+30x+8\sqrt{5}$

Answer 1

Consider the given expression,

$\Rightarrow 5\sqrt{5}{x}^2+30x+8\sqrt{5}$

$\Rightarrow 5\sqrt{5}{x}^2+20x+10x+8\sqrt{5}$

$\Rightarrow 5\sqrt{5}{x}^2+4.\sqrt{5}.\sqrt{5}x+2.\sqrt{5}\sqrt{5}x+8\sqrt{5}$

$\Rightarrow \sqrt{5}x(x+4\sqrt{5})+2.\sqrt{5}(x+4\sqrt{5})$

$\Rightarrow (x+4\sqrt{5})(\sqrt{5}x+2\sqrt{5})$

When,

$(x+4\sqrt{5})=0$

$x=-4\sqrt{5}$

When,

$(\sqrt{5}x+2\sqrt{5})=0$

$x=-2$

Hence, this is the answer.