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Determine p so that the equation x 2 + 5px + 16 = 0 has on real root.
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- 4 < p < 4 . 5 5 -
- 8 < p < 8 . 5 5 -
p < - 4 or p > 4 5 5 - None of these
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Correct Option: B
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 = 16
If 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 < | |
| ⇒ p 2 - | < 0 | |
| ⇒ |  | p - |  | | p + | | < 0 | ||
| 5 | 5 |
| ⇒ either p - | > 0 and p + | < 0 | ||
| ⇒ p > | and p < - | , | ||
Which is not Possible
| ⇒ p - | > 0 and p + | < 0 | ||
| ⇒ p < | and p > - | , | ⇒ - | < p < | . | ||||
Therefore , required answer will be option B .
