Question

Find a quadratic polynomial whose sum and product of zeroes are $\sqrt{2}$ and 3 respectively.

Answer 1

Given ,Sum of roots$=\alpha +\beta =\frac{-b}{a}=\sqrt{2}$

Product of roots$=\alpha \beta =\frac{c}{a}=3$

Polynomial: $p\left(x\right)=x^2-(\alpha +\beta )x+\alpha \beta =0$

$p\left(x\right)=x^2-\sqrt{2}x+3$