Question
For which value of k does the quadratic equation
x² − 4(k + 1)x + (3k² + 8k + 4) = 0 have equal real roots?Solution
ATQ, For equal roots, discriminant D = 0. D = [−4(k + 1)]² − 4·1·(3k² + 8k + 4) = 16(k + 1)² − 4(3k² + 8k + 4) = 16(k² + 2k + 1) − 12k² − 32k − 16 = 16k² + 32k + 16 − 12k² − 32k − 16 = 4k². Set D = 0 ⇒ 4k² = 0 ⇒ k = 0.
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