Question

Find a quadratic polynomial, whose sum and product of zeros are $-\frac{-10}{\sqrt{3}}$ and $7$ respectively

• A. $x^2+\frac{10}{\sqrt{3}}x+\frac{7}{\sqrt{3}}$
• B. $\sqrt{3}{x}^2-10x+7\sqrt{3}$
• C. $\sqrt{3}{x}^2+10x+7\sqrt{3}$
• D. $x^2+10x+7\sqrt{3}$

Answer 1

Answer: (C)

$\sqrt{3}{x}^2+10x+7\sqrt{3}$

If $\alpha ,\beta$ are roots of the quadratic equation, then the equation can be written as :$x^2-x(\alpha +\beta )+\alpha \beta =0$

Similarly, the quadratic equation for above problem is :

$x^2-x\left(\frac{-10}{\sqrt{3}}\right)+7=0$

$\Rightarrow \sqrt{3}{x}^2+10x+7\sqrt{3}=0$