AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) is the common root of the quadratic equations \(x^2-5 x+4 a=0\), \(x^2-2 a x-8=0\), where \(a \in \mathbb{R}\), then the value of \(\alpha^4-\alpha^3+68\) is
- A \(260\)
- B \(250\)
- C \(0\)
- D \(240\)
Answer & Solution
Correct Answer
(A) \(260\)
Step-by-step Solution
Detailed explanation
\(\alpha^2-5\alpha+4a=0 \quad (1)\) \(\alpha^2-2a\alpha-8=0 \quad (2)\) From (1): \(4a = 5\alpha-\alpha^2\) From (2): \(2a = \frac{\alpha^2-8}{\alpha} \Rightarrow 4a = \frac{2(\alpha^2-8)}{\alpha}\) \(5\alpha-\alpha^2 = \frac{2(\alpha^2-8)}{\alpha}\)…
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