AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) are the irrational roots of the equation \(x^5-5 x^4+9 x^3-9 x^2+5 x-1=0\), then the roots of the equation \((\alpha+\beta) x^2+2 \alpha \beta x-\alpha \beta=0\) are
- A \(-1, \frac{1}{3}\)
- B \(\frac{3 \pm \sqrt{5}}{2}\)
- C \(\frac{1 \pm i \sqrt{3}}{2}\)
- D \(1,-\frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(-1, \frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Given equation, \[ x^5-5 x^4+9 x^3-9 x^2+5 x-1=0 \] \(x=1\) is one root of equation. So, \((x-1)\left(x^4-4 x^3+5 x^2-4 x+1\right)=0\) \[ \Rightarrow \quad x^4-4 x^3+5 x^2-4 x+1=0 \] On dividing by \(x^2\), we get,…
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