lf $α, β$ are the roots of the equation $2 x^{2} + 3 x - 4 = 0$ , then the equation whose roots are $3 α + 4 β; 4 α + 3 β$ , is:

2 x^{2} + 21 x + 50 = 0

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2 x^{2} - 21 x + 50 = 0

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2 x^{2} + 21 x + 58 = 0

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2 x^{2} - 21 x + 58 = 0

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Solution

The correct option is A $2 x^{2} + 21 x + 50 = 0$
$x^{2} - (3 α + 4 β + 4 α + 3 β) x + 12 α^{2} + 12 β^{2} + 2 α β = 0$
$x^{2} - (7) (α + β) x + 12 {(α + β)}^{2} - 2 α β) + 2 α β = 0$
$x^{2} - (7) (α + β) x + 12 {(α + β)}^{2} + (α β) = 0$
$α + β = \frac{- 3}{2}$
$α β = - 2$
$x^{2} + 2 \frac{21^{x}}{2} + \frac{6 \times 9}{2} - 2 = 0$
$2 x^{2} + 21 x + 50 = 0$

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