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Relations Between Roots and Coefficients

If α, β are t...

Question

If $α, β$ are the roots of the equation $4 x^{2} + 3 x + 7 = 0$ , then find the value of $α^{2} β + β^{2} α$

$\frac{(- 16)}{21}$

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$\frac{16}{21}$

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$\frac{21}{16}$

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$\frac{(- 21)}{16}$

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Solution

The correct option is D
$\frac{(- 21)}{16}$

$α + β = \frac{- 3}{4} α β = \frac{7}{4} α^{2} β + β^{2} α = α β (α + β) = \frac{- 3}{4} \times \frac{7}{4} = \frac{- 21}{16}$

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