AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(x^3-6 x^2+11 x-6=0\) are \(\alpha, \beta\) and \(\gamma\). Then the equation whose roots are \(\alpha^2, \beta^2, \gamma^2\) among the following is
- A \(x^3+14 x^2+49 x-36=0\)
- B \(x^3-14 x^2+49 x-36=0\)
- C \(x^3-14 x^2-49 x+36=0\)
- D \(x^3-14 x^2-49 x-36=0\)
Answer & Solution
Correct Answer
(B) \(x^3-14 x^2+49 x-36=0\)
Step-by-step Solution
Detailed explanation
It is given that roots of the equation \(x^3-6 x^2+11 x-6=0\) are \(\alpha, \beta, \gamma\). Now, to find the equation whose roots are \(\alpha^2, \beta^2, \gamma^2\), put \(\alpha^2=x \Rightarrow \alpha=\sqrt{x}\). Since, \(\alpha\) is the root of the given equation, so…
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