AP EAMCET · Maths · Quadratic Equation
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \(x^3-a x^2+a x-1=0\) is identical with this cubic equation, then ' \(a\) ' =
- A \(\frac{1}{3}\)
- B 3
- C \(\frac{1}{2}\)
- D 2
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
Let the roots of \(x^3-a x^2+a x-1=0\) be \(\alpha, \beta, \gamma\). \(\alpha + \beta + \gamma = a\) \(\alpha\beta + \beta\gamma + \gamma\alpha = a\) \(\alpha\beta\gamma = 1\) The equation whose roots are \(\alpha^2, \beta^2, \gamma^2\) is identical to the original equation. Sum…
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