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Question
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
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Solution
2x2 + 3x + p = 0
Here, a = 2, b = 3, c = p
b2 - 4ac
= (3)2 - 4 x 2x p
= 9 - 8p
∵ Roots are real
∴ b2 - 4ac > 0
⇒ 9 - 8p ≥ 0
9 ≥ 8p
⇒ 8p ≤ 9
⇒ p ≤ `(9)/(8)`.
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