Search any question & find its solution
Question:
Answered & Verified by Expert
If \(\alpha, \beta\) are the roots of the equation \(\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0\), then the roots of the equation \(\mathrm{ax}^2+\mathrm{bx}(\mathrm{x}+1)+\mathrm{c}(\mathrm{x}+1)^2=0\) are
Options:
Solution:
2334 Upvotes
Verified Answer
The correct answer is:
\(\frac{\alpha}{1-\alpha}, \frac{\beta}{1-\beta}\)
The second equation can be rewritten as
\(a\left(\frac{x}{x+1}\right)^2+b\left(\frac{x}{x+1}\right)+c=0\)
and hence its roots correspond to \(\frac{\mathrm{x}}{\mathrm{x}+1}=\alpha\) and \(\frac{x}{x+1}=\beta\).
Hence \(x=\frac{\alpha}{1-\alpha}\) and \(\frac{\beta}{1-\beta}\).
\(a\left(\frac{x}{x+1}\right)^2+b\left(\frac{x}{x+1}\right)+c=0\)
and hence its roots correspond to \(\frac{\mathrm{x}}{\mathrm{x}+1}=\alpha\) and \(\frac{x}{x+1}=\beta\).
Hence \(x=\frac{\alpha}{1-\alpha}\) and \(\frac{\beta}{1-\beta}\).
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.