Question

Write the polynomial, the product and sum of whose zeroes are $-\frac{9}{2} and -\frac{3}{2}$ respectively.

Answer 1

$<b>$

Given,
Sum of zeroes of polynomial = $-\frac{3}{2}$
& Product of Zeroes of polynomial = $-\frac{9}{2}$


We have,
For a quadratic polynomial ,
$ax^{2} + bx+c$
Sum of Roots = $\frac{-b}{a}$
Product of Roots = $\frac{c}{a}$

Let $\alpha$ &$\beta$ be the zeroes (or Roots) of polynomial

Polynomial in terms of Zeroes = $k[x^{2} - (\alpha+\beta)x + \alpha\beta]$

$\implies k[x^{2} - (-\frac{9}{2})x + (\frac{-3}{2})]$

$\implies k [x^{2} + \frac{9}{2}x - \frac{3}{2}]$

$\implies \frac{k}{2} [2x^{2} + 9x - 3]$