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Ifthe roots of a quadratic equation $a x^{2}+b x+c=0$ are $\alpha$ and $\beta$, then the quadratic equation having roots $\alpha^{2}$ and $\beta^{2}$ is
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The correct answer is:
$a^{2} x^{2}-\left(b^{2}-2 a c\right) x+c^{2}=0$
Quadratic equation is given by $\mathrm{x}^{2}-($ sum of roots $) \mathrm{x}+($ product of roots $)=0$ Required equation is $\mathrm{x}^{2}-\mathrm{x}\left(\alpha^{2}+\beta^{2}\right)+(\alpha \beta)^{2}=0$
$\Rightarrow \mathrm{x}^{2}-\mathrm{x}\left[(\alpha+\beta)^{2}-2 \alpha \beta\right]+(\alpha \beta)^{2}=0$
$\Rightarrow \mathrm{x}^{2}-\mathrm{x}\left(\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}-\frac{2 \mathrm{c}}{\mathrm{a}}\right)+\frac{\mathrm{c}^{2}}{\mathrm{a}^{2}}=0$
$\Rightarrow \mathrm{a}^{2} \mathrm{x}^{2}-\mathrm{x}\left(\mathrm{b}^{2}-2 \mathrm{ac}\right)+\mathrm{c}^{2}=$
$\Rightarrow \mathrm{x}^{2}-\mathrm{x}\left[(\alpha+\beta)^{2}-2 \alpha \beta\right]+(\alpha \beta)^{2}=0$
$\Rightarrow \mathrm{x}^{2}-\mathrm{x}\left(\frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}-\frac{2 \mathrm{c}}{\mathrm{a}}\right)+\frac{\mathrm{c}^{2}}{\mathrm{a}^{2}}=0$
$\Rightarrow \mathrm{a}^{2} \mathrm{x}^{2}-\mathrm{x}\left(\mathrm{b}^{2}-2 \mathrm{ac}\right)+\mathrm{c}^{2}=$
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