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1. Find the roots of the quadratic equationFind the value of k, for which one root of the quadratic equation kx2 - 14x + 8 is six timesthe other |
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Answer» The given equation is » kx² - 14x + 8 = 0 Divide the equation THROUGHOUT by K. » x² - 14x/k + 8/k = 0 Let the two roots be A and 6A. According to the given condition. Sum of roots = -b/a => A + 6A = 14/k » 7A = 14/k » A = 2/k ... (1) PRODUCT of the roots = c/a => A × 6A = 8/k => 6A² = 8/k ... (2) Substitute (1) in (2) » 6 (2/k)² = 8/k » 6/k² = 8/k » k = 3/4 Substitute in eq (1) A = 2/k = (3/4) / 2 = 3/8 6A = 9/4 Therefore, roots are 3/8 and 9/4. |
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