Question

Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively.

$-\sqrt{3},\frac{1}{4}$

• A. $2x^2+4\sqrt{3}x+4$
• B. $x^2-4\sqrt{3}x+4$
• C. $4x^2+4\sqrt{3}x+1$
• D. $2x^2+4\sqrt{3}x+1$

Answer 1

The correct option is C $4x^2+4\sqrt{3}x+1$

Given,

Sum of the roots=$-\sqrt{3}$

Product of the roots=$\frac{1}{4}$

Now,the quadratic equation is given by,

$x^2-$(sum of roots)$x$+(product of the roots)$=0$

$\Rightarrow x^2-(-\sqrt{3})x+\frac{1}{4}=0$

$\Rightarrow \frac{4x^2+4\sqrt{3}+1}{4}=0$

$\Rightarrow \frac{1}{4}(4x^2+4\sqrt{3}+1)=0$

$\Rightarrow (4x^2+4\sqrt{3}+1)=0$

The above equation is the required quadratic equation.