AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^3-13 x^2+k x+189=0\) such that \(\beta-\gamma=2\), then \(\beta+\gamma: \mathrm{k}+\alpha=\)
- A \(4: 3\)
- B \(2: 1\)
- C \(6: 5\)
- D \(3: 4\)
Answer & Solution
Correct Answer
(A) \(4: 3\)
Step-by-step Solution
Detailed explanation
\(\alpha+\beta+\gamma=13\) \(\beta-\gamma=2\) \(\Rightarrow \beta = (15-\alpha)/2\), \(\gamma = (11-\alpha)/2\) \(\alpha\beta\gamma = -189 \Rightarrow \alpha \left(\frac{15-\alpha}{2}\right) \left(\frac{11-\alpha}{2}\right) = -189\)…
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