Question

If $(2+i\sqrt{3})$ is a root of the equation $x^2+px+q=0$, then the values of $p$ and $q$ are

• A. $4$ and $7$
• B. $-4$ and $-7$
• C. $-4$ and $7$
• D. $4$ and $-7$

Answer 1

Answer: (C)

$-4$ and $7$

Given equation is $x^2+px+q=0$
Let $\alpha =2+i\sqrt{3}$ (given)
Then, $\beta =2-i\sqrt{3}$
Now, $\alpha +\beta =-p$
$2+i\sqrt{3}+2-i\sqrt{3}=-p$
$\Rightarrow 4=-p$ or $p=-4$
Also, $\alpha \beta =q$
$(2+i\sqrt{3})(2-i\sqrt{3})=q$
$\Rightarrow 7=q$
Hence, option 'C' is correct.