Search any question & find its solution
Question:
Answered & Verified by Expert
$2 x^{2}+3 x-\alpha-0$ has roots $-2$ and $\beta$ while the equation $x^{2}-3 m x+$ $2 \mathrm{~m}^{2}=0$ has both roots positive, where $\alpha>0$ and $\beta>0$.
What is the value of $\alpha ?$
Options:
What is the value of $\alpha ?$
Solution:
1749 Upvotes
Verified Answer
The correct answer is:
2
$2 x^{2}+3 x-\alpha=0$
Its roots are: $-2 \& \beta .$
i.e., $\frac{-3}{2}=\beta-2 \Rightarrow \beta=2-\frac{3}{2}=\frac{1}{2} \Rightarrow \beta=\frac{1}{2}$
$\frac{\alpha}{2}=2 \beta \Rightarrow \alpha=4 \times \frac{1}{2} \Rightarrow \alpha=2$
Its roots are: $-2 \& \beta .$
i.e., $\frac{-3}{2}=\beta-2 \Rightarrow \beta=2-\frac{3}{2}=\frac{1}{2} \Rightarrow \beta=\frac{1}{2}$
$\frac{\alpha}{2}=2 \beta \Rightarrow \alpha=4 \times \frac{1}{2} \Rightarrow \alpha=2$
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.