# Q2 (2)   Find a quadratic polynomial each with the given numbers as the sum and product of zeroes respectively. $\sqrt 2 , 1/3$

$\\\alpha +\beta =\sqrt{2}\\ \alpha \beta =\frac{1}{3}$
$\\x^{2}-(\alpha +\beta )+\alpha \beta =0\\ x^{2}-\sqrt{2}x+\frac{1}{3}=0\\ 3x^{2}-3\sqrt{2}x+1=0$
The required quadratic polynomial is $3x^{2}-3\sqrt{2}x+1$