NumericalModerate3 marks
Find the value of k for which the following equation has equal roots. x² + 4kx + (k² - k + 2) = 0
Topic: Quadratic equations
Previous-year question practice database
Answer
Exam answer
k = –1, k = 2/3
Explanation
Given equation is x2 + 4kx + (k2 – k + 2) = 0 For equal roots discriminant = 0 ∴ (4k)2 – 4(k2 – k + 2) = 0 16k2 – 4k2 + 4k – 8 = 0 12k2 + 4k – 8 = 0 3k2 + k – 2 = 0 ⇒ 3k2 + 3k – 2k = 0 3k(k + 1)(3k – 2) = 0 ∴ k = –1, k = 2/3
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