Question

Find the value of b, if one root of the equation $x^2$ + ax + 2b = 0 is 2 + 4i, where a, b ∈ R

• A. 20
• B. -20
• C. -10
• D. 10

Answer 1

The correct option is D

10

If 2 + 4i is a root, the other root will be 2 - 4i

Product of the roots = 2b

⇒ (2 + 4i) (2 - 4i) = 2b

or

2b = $2^2$ - ${\left(4i\right)}^2$

= 4 - $4^2$× $i^2$

= 4 - 16 × -1

= 4 + 16

⇒ 2b = 20

⇒ b = 10