Question

Find the Quadratic Polynomial whose sum of zeroes is $-\frac{3}{2}$ and product is -1

Answer 1

Given sum of zeroes $=\alpha +\beta =\frac{-b}{a}=\frac{-3}{2}$

Product of zeroes$=\alpha \cdot \beta =\frac{c}{a}=-1$

Polynomial: $p\left(x\right)=x^2-(\alpha +\beta )x+\alpha \beta$

$\Rightarrow p\left(x\right)=x^2+\frac{3}{2}x+(-1)=0$

$\Rightarrow p\left(x\right)=2x^2+3x-1=0$