AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) is a common root of \(x^2-5 x+\lambda=0\) and \(x^2-8 x-2 \lambda\) \(=0(\lambda \neq 0)\) and \(\beta, \gamma\) are the other roots of them, then \(\alpha+\beta+\gamma+\lambda=\)
- A 0
- B -1
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(\alpha\) is root of \(x^2-5 x+\lambda=0\) and \(x^2-8 x-2 \lambda=0\) \(\Rightarrow \alpha^2-5 \alpha+\lambda=0\)...(i) and \(\alpha^2-8 \alpha-2 \lambda=0\)...(ii) Subtracting (ii) from (i), we get \(3 \alpha+3 \lambda=0 \Rightarrow \alpha=-\lambda\) As \(\alpha\) is root of…
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