Question

Find zeros of quadratic polynomial 5 root 5x^2+30x+8root5​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• $p(x) = 5\sqrt{5}x^2 + 30x + 8\sqrt{5}$

To Find:

• Zeroes of p(x)

Solution:

$p(x) = 5\sqrt{5}x^2 + 30x + 8\sqrt{5} \\\\\implies p(x) = 0 \\\\\implies 5\sqrt{5}x^2 + 30x + 8\sqrt{5} = 0$

$5\sqrt{5}x^2 + 30x + 8\sqrt{5} = 0 \\\\\implies x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\\\ \text{Here, a = 5\sqrt{5} , b = 30 and c = 8\sqrt{5} }$

$\\\\\implies x = \dfrac{-30 \pm \sqrt{30^2 - 4(5\sqrt{5})(8\sqrt{5})}}{2(5\sqrt{5})}$

$\\\\\implies x = \dfrac{-30 \pm \sqrt{900 - 800}}{10 \sqrt{5}}$

$\\\\\implies x = \dfrac{-30 \pm 10}{10\sqrt{5}} \\\\\implies x = \dfrac{-3 \pm 1}{\sqrt{5}} \\\\\bf{\implies x = \dfrac{-4*\sqrt{5}}{5} \:\:\:\:\: or\:\:\:\:\: x = \dfrac{-2*\sqrt{5}}{5}}</p><p>$

Hope it helps!!