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Question
Find the values of p for which the equation 3x2 – px + 5 = 0 has real roots.
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Solution
3x2 – px + 5 = 0
Here, a = 3, b = -p, c = 5
∴ b2 - 4ac
= (-p)2 - 4 x 3 x 5
= p2 - 60
∴ Roots are real
∴ b2 - 4ac ≥ 0
∴ p2 - 60 ≥ 0
⇒ p2 ≥ 60
⇒ `p ≥ ± sqrt(60) = ±2sqrt(15)`
∴ `p ≤ -2sqrt(15) or p ≥ 2sqrt(15)`.
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