If - - are the roots of the equation 3 x2-5 x-4-0- then the quadratic equation whose roots are -2- -2A- 9 x2-x-16-0B- 9 x2-x-24-0C- 9 x2-x-16-0D- 9 x2-x-24-0

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Inequalities Involving Modulus Function

If α, β are t...

Question

If $α, β$ are the roots of the equation $3 x^{2} + 5 x + 4 = 0$ , then the quadratic equation whose roots are $α^{2}, β^{2}$

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Solution

The correct option is C

$α + β = \frac{- 5}{3}, α β = \frac{4}{3}$

To find the equation whose roots are $α^{2}, β^{2}$ we have to find $α^{2} + β^{2}$ and $α^{2} β^{2}$

$α^{2} + β^{2} = (α + β)^{2} - 2 α β = \frac{25}{9} - \frac{2 \times 4}{3} = \frac{1}{9} α^{2} β^{2} = \frac{16}{9} \Rightarrow The equation is x^{2} - \frac{1}{9} x + \frac{16}{9} = 0 9 x^{2} - x + 16 = 0$

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If α,β are the roots of the equation 3x2+5x+4=0, then the quadratic equation whose roots are α2,β2

The correct option is C α+β=−53,αβ=43 To find the equation whose roots are α2,β2 we have to find α2+β2 and α2β2 α2+β2=(α+β)2−2αβ=259−2×43=19α2β2=169⇒The equation isx2−19x+169=09x2−x+16=0

If $α, β$ are the roots of the equation $3 x^{2} + 5 x + 4 = 0$ , then the quadratic equation whose roots are $α^{2}, β^{2}$