Search any question & find its solution
Question:
Answered & Verified by Expert
If the equation $x^{2}+k x+1=0$ has the roots $\alpha$ and $\beta$, then what is the value of $(\alpha+\beta) \times\left(\alpha^{-1}+\beta^{-1}\right) ?$
Options:
Solution:
2113 Upvotes
Verified Answer
The correct answer is:
$\mathrm{k}^{2}$
As given: Roots of the equations $x^{2}+k x+1=0$ are $\alpha$ and $\beta .$ Given expression $(\alpha+\beta)\left(\alpha^{-1}+\beta^{-1}\right)=(\alpha+\beta)\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)$
$=(\alpha+\beta)\left(\frac{\alpha+\beta}{\alpha \beta}\right)=\frac{(\alpha+\beta)^{2}}{\alpha \beta}=\frac{(-k)^{2}}{1}=\mathrm{k}^{2}$
$=(\alpha+\beta)\left(\frac{\alpha+\beta}{\alpha \beta}\right)=\frac{(\alpha+\beta)^{2}}{\alpha \beta}=\frac{(-k)^{2}}{1}=\mathrm{k}^{2}$
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.