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Question

If p and q are the roots of 2x2+3x+4 = 0, then find the value of p2q+q2p

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Solution

For a quadratic equation given by ax2+bx+c = 0,
the sum of the roots = -ba,
the product of the roots = ca.

Given, quadratic equation: 2x2+3x+4 = 0,
here, a = 2, b = 3, c = 4

Here, p+q = sum of the roots = -ba = -32
Here, pq = product of the roots = ca = 42 = 2.

p2q+q2p = pq(p+q) = -32×2 = -3.

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