Question

If 1 – i is a root of the equation $x^{2} + ax + b = 0$, then the values of a and b are

• A. 2, 1
• B. – 2, 2
• C. 2, 2
• D. 2, – 2

Answer 1

Answer: (B)

– 2, 2

Answer 2

Since $1 - i$ is a root of $x^{2} + ax + b = 0$. ∴ $\mathbf{1 + i}$ is also a root.

Sum of roots ⇒ $1 - i + 1 + i = - a$ ⇒ $a = - 2$

Product of roots ⇒ $(1 - i)(1 + i) = b$ ⇒ $b = 2$

Hence $a = - 2$, $b = 2$