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If x2 + 5px + 16 has no real roots, then |
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Answer» The GIVEN quadratic equation is x 2 + 5px + 16 = 0 ........(1)Comparing it with ax 2 + bx + c = 0, we get a = 1, b = 5P, c = 16If equation (1) has no real roots, then discriminant ( D ) < 0⇒ b 2 - 4ac < 0 ⇒ (5p) 2 - 4 × (1) × (16) < 0⇒ 25p 2 - 64 < 0 ⇒ 25p 2 < 64⇒ p 2 < 6425⇒ p 2 - 64< 025⇒ p - 8 p + 8 < 05 5⇒ EITHER p - 8> 0 and p + 8< 055⇒ p > 8and p < - 8,55Which is not Possible⇒ p - 8> 0 and p + 8< 055⇒ p < 8and p > - 8, ⇒ - 8< p < 8.5555Therefore , required answer will be option B . |
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