Find the value of k if the roots of x² – 3x + k + 1 = 0 differ by unity?
- –3
- 1
- 2
- None of these
Explanation
Let's use the quadratic formula to find the roots:
x = (-b ± √(b² - 4ac)) / 2a
For the given equation x² - 3x + k + 1 = 0:
a = 1, b = -3, c = k + 1
The roots differ by unity, so:
√(b² - 4ac) = 1
(-3)² - 4(1)(k + 1) = 1
9 - 4k - 4 = 1
5 - 4k = 1
-4k = -4
k = 1
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