If the equation $x^{2}-c x+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+a x+b=0$ , where $a^{2}>4 b$ , then the roots of $x^{2}-4 b x+2 b^{2}-c=0$ will be

Question

If the equation $x^{2}-c x+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+a x+b=0$ , where $a^{2}>4 b$ , then the roots of $x^{2}-4 b x+2 b^{2}-c=0$ will be

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kritika · Answer 1 · 2021-12-27T07:30:07+0000

Ans: (A, D)
Hint :

$x^{2}-4 b x+2 b^{2}-c=0$
let

$\alpha_{1}, \beta_{1}$ be roots

$\begin{aligned} \alpha_{1}, \beta_{1} &=2 b^{2}-c \\ &=2 b^{2}-\left(a^{4}-4 a^{2} b+2 b^{2}\right) \\ &=a^{2}\left(4 b-a^{2}\right)<0 \end{aligned}$
Hence one positive and one negative

If the equation $x^{2}-c x+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+a x+b=0$ , where $a^{2}>4 b$ , then the roots of $x^{2}-4 b x+2 b^{2}-c=0$ will be

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