Question

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

Answer 1

Sum of roots$=-\frac{9}{2}$
Product of root $=-\frac{3}{2}$
Polynomial is,
$\begin{array}{c}{x}^2-\left(\frac{9x}{2}\right)+\left(-\frac{3}{2}\right)=0\\ x^2+\frac{9x}{2}-\frac{3}{2}=0\\ 2x^2+9x-3=0\end{array}$