Question

Find the quadratic polynomial whose zeroes are $-\frac{2}{\sqrt{3}}$ and $\frac{\sqrt{3}}{-4}$.

Answer 1

given the zeroes are $-\frac{2}{\sqrt{3}}$ and $\frac{\sqrt{3}}{-4}$

We know that a quadratic polynomial having roots $\alpha$ and $\beta$ is given by $K(x-\alpha )(x-\beta )$

So, the required polynomial is $k(x+\frac{2}{\sqrt{3}})(x+\frac{\sqrt{3}}{4})$

$k(x^2+\frac{2}{\sqrt{3}}x+\frac{\sqrt{3}}{4}x+\frac{1}{2})$

$=k(x^2+\frac{11}{4\sqrt{3}}x+\frac{1}{2})$