Question

Find the zeroes of the polynomial p ( x ) = √3x^2 + 10x + 7√3

Answer 1

$Given : p(x) = \sqrt{3}x^2 + 10x + 7\sqrt{3}$

Zero of the polynomial is the value of x where p(x) = 0.

$=> \sqrt{3}x^2 + 10x + 7\sqrt{3} = 0$

$=> \sqrt{3}x^2 + 7x + 3x + 7\sqrt{3} = 0$

$=>x(\sqrt{3}x + 7) + \sqrt{3}(\sqrt{3}x + 7) = 0$

$=> (x + \sqrt{3})(\sqrt{3}x + 7) = 0$

$=> x = -\sqrt{3},x = \frac{-7}{\sqrt{3} }$

Therefore, The zeroes of the polynomial are:

$=> \boxed{\alpha=-\sqrt{3},\beta=\frac{-7}{\sqrt{3}}}$

Hope it helps!