If $\alpha, \beta, \gamma$ are the roots of $f(x)=x^3-9 x^2+26 x$ -24, then $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ are the roots of

Question

If $\alpha, \beta, \gamma$ are the roots of $f(x)=x^3-9 x^2+26 x$ -24, then $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ are the roots of, $24 x^3+26 x^2+9 x-1$, $24 x^3-26 x^2+9 x-1$, $24 x^3+26 x^2-9 x-1$, $24 x^3-26 x^2+9 x+1$

MARKS App · Accepted Answer

It is given that roots of $f(x)=x^3-9 x^2+26 x-24$ are $\alpha, \beta, \gamma$, then the equation, where roots are $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$. We can obtain by dividing $f(x)$ by $x^3$, so required equation is $24 x^3-26 x^2+9 x-1$. Hence, option (b) is correct.

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