Search any question & find its solution
Question:
Answered & Verified by Expert
The quadratic equation
$2 x^{2}-\left(a^{3}+8 a-1\right) x+a^{2}-4 a=0$ has roots of opposite sign. Then,
Options:
$2 x^{2}-\left(a^{3}+8 a-1\right) x+a^{2}-4 a=0$ has roots of opposite sign. Then,
Solution:
2536 Upvotes
Verified Answer
The correct answer is:
$0 < a < 4$
Since, roots are opposite sign.
Product of the roots $\leq 0$ $\begin{array}{ll}\Rightarrow & a^{2}-4 a < 0 \\ \Rightarrow & a(a-4) < 0 \\ \Rightarrow & 0 < a < 4\end{array}$
Product of the roots $\leq 0$ $\begin{array}{ll}\Rightarrow & a^{2}-4 a < 0 \\ \Rightarrow & a(a-4) < 0 \\ \Rightarrow & 0 < a < 4\end{array}$
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.