Question

Find a quadratic polynomial whose sum and product respectively of the zeros are as given. Also, find the zeros of these polynomials by
$\frac{-8}{3},\frac{4}{3}$

Answer 1

Let $a$ and $b$ be the zeros of the required polynomial.

Given,

$a+b=-\frac{8}{3}$.....(1) and $ab=\frac{4}{3}$......(2).

Now the polynomial whose zeros are $a$ and $b$ be

$x^2-(a+b)x+ab$

$=x^2+\frac{8}{3}x+\frac{4}{3}$.[Using (1) and (2)].

Now solving (1) and (2) we get,

$a=-\frac{2}{3}$ or $-2$ and $b=-2$ or $-\frac{2}{3}$.

So, $-\frac{2}{3}$ and $-2$ are the zeros of the polynomial.