AP EAMCET · Maths · Quadratic Equation
Let \(a, b\) and \(c\) be positive real numbers. If \(\frac{x^2-b x}{a x-c}=\frac{m-1}{m+1}\) has two roots which are numerically equal but opposite in sign, then the value of \(m\) is
- A \(c\)
- B \(\frac{1}{c}\)
- C \(\frac{a+b}{a-b}\)
- D \(\frac{a-b}{a+b}\)
Answer & Solution
Correct Answer
(D) \(\frac{a-b}{a+b}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Given, } \frac{x^2-b x}{a x-c}=\frac{m-1}{m+1} \\ & \Rightarrow\left(x^2-b x\right)(m+1)=(m-1)(a x-c) \\ & \Rightarrow x^2(m+1)-x(b(m+1)+a(m-1)+c(m-1)=0 \end{aligned} \] Let \(p\) and \(-p\) are roots of Eq. (i), then…
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