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Find the value of k for which one root of the quadratic equation kx2-14x + 8 = 0 is six times the other. |
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Answer» Let roots beα andβA/qα = 6βnow, ifα andβ are roots then equation will be (x -α)(x -β) =0(x -α)(x -β) =0⇒ x² - (α+β)x +αβ =0now puttingα = 6β ,⇒x² - (6β +β)x + 6β×β =0⇒x² - 7βx +6β² =0now comparing with kx² -14x +8 =07β =14/k⇒β =2/k ⇒β² = 4/k²_______(1)and 6β² =8/k⇒β² =4/3k_______(2)equating (1) and (2), we get,4/k² = 4/3k⇒k =3 |
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