Question

If $4-5i$ is a root of the quadratic equation $x^2+ax+b=0$, then $(a,b)$ is equal to:

• A. $(8,41)$
• B. $(-8,41)$
• C. $(41,8)$
• D. $(-41,8)$

Answer 1

Answer: (B)

$(-8,41)$

Fact: Imaginary root occurs in conjugate pair

So if one root is $4-5i$, then another root will be $4+5i$

Hence, sum of roots is $-a=8\Rightarrow a=-8$

And product of roots is $b=(4+5i)(4-5i)=4^2+5^2=41$

$\therefore (a,b)=(-8,41)$