Question

Obtain a quadratic polynomial $p\left(x\right)=a{x}^2+bx+c$, where sum of zeros is $\sqrt{2}$ and product of zeros is $\frac{1}{3}$; $a<0$.

Answer 1

Given,

$sum-of-roots=\sqrt{2}$

$product-of-roots=\frac{1}{3}$

we have,

$p\left(x\right)=x^2-(sum-of-roots)x+(product-of-roots)$

$x^2-\sqrt{2}x+\frac{1}{3}=0$

$\therefore 3x^2-3\sqrt{2}x+1=0$