AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of \(a x^2+b x+c=0\), then the roots of \(a x^2-b x(x-1)+c(x-1)^2=0\) are
- A \(\frac{\alpha+1}{\alpha}, \frac{\beta+1}{\beta}\)
- B \(\frac{\alpha}{\alpha+1}, \frac{\beta}{\beta+1}\)
- C \(\frac{\alpha}{\beta}, \frac{\beta}{\alpha}\)
- D \(\frac{\alpha-1}{\alpha+1}, \frac{\beta-1}{\beta+1}\)
Answer & Solution
Correct Answer
(B) \(\frac{\alpha}{\alpha+1}, \frac{\beta}{\beta+1}\)
Step-by-step Solution
Detailed explanation
\(a \left(\frac{x}{x-1}\right)^2 - b \left(\frac{x}{x-1}\right) + c = 0\) Let \(y = \frac{x}{x-1}\). \(a y^2 - b y + c = 0\) If \( \alpha, \beta \) are roots of \(a X^2 + b X + c = 0\), then \( -\alpha, -\beta \) are roots of \(a y^2 - b y + c = 0\).…
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