Question
What are the values of k, if the roots of the equation
x² + 2(k - 4)x + 2k = 0 are equal?Solution
Given, the roots of the equation x² + 2(k - 4)x + 2k = 0 are equal. When roots are equal then b² = 4ac ⇒ [2(k - 4)]² = 4 * 1 * 2k ⇒ 4(k - 4)² = 8k ⇒ k² - 8k + 16 = 2k ⇒ k² - 10k + 16 = 0 ⇒ (k - 2) (k - 8) = 0 ⇒ k = 2, 8
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