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If -5 is a root of the quadratic equation 2x2 + 2px - 15 = 0 and the quadratic equation p (x2 + x) + k = 0 has equal roots, find the value of k. |
Answer» 2x2 + 2px - 15 = 0 Put x = –5 2(–5)2 + 2p(–5) - 15 = 0 50 – 10p – 15 = 0 35 = 10p p = 3.5 Equation p (x2 + x) + k = 0 has equal roots i.e. d = 0 p (x2 + x) + k = 0 p = 3.5 3.5 (x2 + x) + k = 0 3.5x2 + 3.5x + k = 0 d = b2 – 4ac d = (3.5)2 – 4(3.5)(k) d = 12.25 – 14k Putting d = 0 ∴ Equation will be: 0 = 12.25 – 14k 14k = 12.25 k = 12.25/14 k = 0.875 |
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