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

3 Answers

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

Your answer

3 Answers

Your comment on this answer:

Your comment on this answer:

Your comment on this answer:

Related questions

Categories