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4-2.Quadratic Equations and Inequations
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If $\alpha , \beta$ and $\gamma$ are the roots of ${x^3} + 8 = 0$, then the equation whose roots are ${\alpha ^2},{\beta ^2}$ and ${\gamma ^2}$ is
A
${x^3} - 8 = 0$
B
${x^3} - 16 = 0$
C
${x^3} + 64 = 0$
D
${x^3} - 64 = 0$.
Solution
(d) Let $y = {x^2}$. Then $x = \sqrt y $
$\therefore$ ${x^3} + 8 = 0\,\, \Rightarrow \,\,{y^{3/2}} + 8 = 0$
==> ${y^3} = 64\,\,\, \Rightarrow \,\,\,{y^3} – 64 = 0$
Thus the equation having roots ${\alpha ^2},{\beta ^2}$ and ${\gamma ^2}$is ${x^3} – 64 = 0$.
Standard 11
Mathematics
