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Question

Find the value(s) of p for which the quadratic equation 2x2+3xp=0 has real roots.

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Solution

The given quadratic equation is,
2x2+3xp=0

Here,
a=2, b=3, c=p

If the equation is supposed to have real roots, then D0. Therefore,
b24ac0
94×2×(p)0
9+8p0
p98

Thus, the values of p for which the equation has real roots are (,98].

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