AP EAMCET · Maths · Quadratic Equation
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
- A \(24 x^3+26 x^2+9 x-1\)
- B \(24 x^3-26 x^2+9 x-1\)
- C \(24 x^3+26 x^2-9 x-1\)
- D \(24 x^3-26 x^2+9 x+1\)
Answer & Solution
Correct Answer
(B) \(24 x^3-26 x^2+9 x-1\)
Step-by-step Solution
Detailed explanation
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,…
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