Question

If 3 - 5i is one root of the equation - $x^2$ + ax + b = 0, find a + b, where a,b∈ R

• A. 24
• B. -34
• C. -28
• D. 34

Answer 1

The correct option is C

-28

Complex roots occur in conjugate pairs.

Since the coefficients are all real, the other root will be conjugate of 3 - 5i i.e. 3 + 5i

Sum of roots = 3 - 5i + 3 + 5i

$\frac{-a}{-1}$ = 6

⇒ a = 6

Products of roots = (3 - 5i) × (3 + 5i)

$\frac{b}{-1}$ = 9 + 25

b = - 34

a+b= -28