Question

If $-i+3$ is a root of $x^2-6x+k=0$, then the value of $k$ is

• A. $5$
• B. $\sqrt{5}$
• C. $\sqrt{10}$
• D. $10$

Answer 1

The correct option is D $10$

Fact: If coefficient of a quadratic equation are rational number , then complex roots occur in conjugate pair,

So other root of given quadratic is, $3+i$

Now product of given quadratic is $=k$

$\Rightarrow k=(3+i)(3-i)=3^2-i^2=9+1=10$