If $\alpha$ and $\beta$ are roots of $a x^{2}+b x+c=0$ then the equation whose roots are $\alpha^{2}$ and $\beta^{2}$ is

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If $\alpha$ and $\beta$ are roots of $a x^{2}+b x+c=0$ then the equation whose roots are $\alpha^{2}$ and $\beta^{2}$ is

3 Answers

deepak01 · Answer 1 · 2021-12-20T11:36:04+0000

Ans: (A)
Let $y=x^{2} \Rightarrow x=\sqrt{y}$
putting $\sqrt{y}$ in the given equation
$$
a y+b \sqrt{y}+c=0 \Rightarrow b \sqrt{y}=-a y-c \quad \Rightarrow b^{2} y=a^{2} y^{2}+c^{2}+2 a c y
$$
$$
\Rightarrow \mathrm{a}^{2} \mathrm{y}^{2}-\left(\mathrm{b}^{2}-2 \mathrm{ac}\right) \mathrm{y}+\mathrm{c}^{2}=0
$$
So the required quadratic equation is $a^{2} x^{2}-\left(b^{2}-2 a c\right) x+c^{2}=0$

If \(\alpha\) and \(\beta\) are roots of \(a x^{2}+b x+c=0\) then the equation whose roots are \(\alpha^{2}\) and \(\beta^{2}\) is

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