If 1 - I, is a root of the equation x² + ax + b = 0, where a, b, ∈ R, then the value of a - b is?
- 1
- 2
- -4
- None of these
Explanation
Given that 1 - i is a root of the equation x² + ax + b = 0, and the coefficients are real, the complex conjugate 1 + i must also be a root.
The sum of the roots = (1 - i) + (1 + i) = 2 = -a
So, a = -2
The product of the roots = (1 - i)(1 + i) = 1² - i² = 1 + 1 = 2 = b
So, b = 2
Now, a - b = -2 - 2 = -4
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