If (1 - i) is a root of the equation x2 + ax + b = 0, where a, b ∈ ℝ, then find the values of a and b.

Question

Shiksha Nation · Accepted Answer

Sum of roots -a/1= (1 - i) + (1 + i) = -2

But sum of roots = -a ⇒ -a = 2 ⇒ a = -2

Product of roots b/1 = (1 - i)(1 + i) = 1 - i² = 1 + 1 = 2

But product of roots = b ⇒ b = 2

Therefore, a = -2 and b = 2

If (1 - i) is a root of the equation x² + ax + b = 0, where a, b ∈ ℝ, then find the values of a and b.