Question

If sum of zeros $=\sqrt{2}$, product of its zeros $=\frac{1}{3}$. The quadratic polynomial is

• A. $3x^2-3\sqrt{2}x+1$
• B. $\sqrt{2}{x}^2+3x+1$
• C. $3x^2-2\sqrt{3}x+1$
• D. $\sqrt{2}{x}^2+x+3$

Answer 1

The correct option is A $3x^2-3\sqrt{2}x+1$

If $\alpha$, $\beta$ be the zeros of the quadratic polynomial $a{x}^2+bx+c$,then $(\alpha +\beta )=\sqrt{2}=-\frac{b}{a},\alpha \beta =\frac{1}{3}=\frac{c}{a}$
If $a=3$, $b=-3\sqrt{2}$, $c=1$, the required polynomial will be $3x^2-3\sqrt{2}x+1$