TS EAMCET · Maths · Quadratic Equation
If \((2-i)\) is one of the roots of the equation \(x^4-9 x^3+31 x^2-49 x+30=0\) and \(\alpha, \beta(\alpha < \beta)\) are its real roots then \(2 \alpha-\beta=\)
- A 3
- B 2
- C 1
- D 0
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Given biquadratic equation is \[ \mathrm{x}^4-9 \mathrm{x}^3+31 \mathrm{x}^2-49 \mathrm{x}+30=0 \] having four roots, \(\alpha, \beta, 2-i\) and \(2+i\) now sum of roots, \(\alpha+\beta+(2-i)+(2+i)=9\) \(\alpha . \beta .(2-i)(2+i)=30\) \(\Rightarrow \alpha+\beta=5\) and…
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