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4x2 - 13x + k = 0, one root is 12 times of another root, then find the value of k? |
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Answer» 4x2 - 13x + k = 0 .....(i) Let roots are α & 12α. ∴ Sum of roots = \(\frac{-(-13)}{4}\) ⇒ \(\alpha + 12\alpha = \frac {13}4\) ⇒ \(13\alpha = \frac{13}4\) ⇒ \(\alpha = \frac 14\) and \(12\alpha = \frac{12}{4} = 3\) Hence, \(\frac14\) & 3 are roots of equation (i). ∴ 4(3)2 - 13 x 3 + k = 0 ⇒ k = 39 - 36 = 3 |
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