Question

If one root of the quadratic equation $x^2-10x+2k=0$ is $5-\sqrt{3},$ find $k$.

• A. $11$
• B. $12$
• C. $13$
• D. $15$

Answer 1

The correct option is A $11$

One of the root of the equation is $5-\sqrt{3}$, then the other is $5+\sqrt{3}$
Product of the roots = $(5+\sqrt{3})(5-\sqrt{3})=2k$
$\Rightarrow 25-3=2k$
$\Rightarrow 22=2k$
$\Rightarrow k=11$