Search any question & find its solution
Question:
Answered & Verified by Expert
If both the roots of $k\left(6 x^2+3\right)+r x+2 x^2-1=0$ and $6 k\left(2 x^2+1\right)+p x+4 x^2-2=0$ are common, then $2 r-p$ is equal to
Options:
Solution:
2574 Upvotes
Verified Answer
The correct answer is:
$0$
Given equation can be written as
$(6 k+2) x^2+r x+3 k-1=0$ ...(i)
and $2(6 k+2) x^2+p x+2(3 k-1)=0$ ...(ii)
Condition for common roots is
$\frac{12 k+4}{6 k+2}=\frac{p}{r}=\frac{6 k-2}{3 k-1}=2$ or
$2 r-p=0$
$(6 k+2) x^2+r x+3 k-1=0$ ...(i)
and $2(6 k+2) x^2+p x+2(3 k-1)=0$ ...(ii)
Condition for common roots is
$\frac{12 k+4}{6 k+2}=\frac{p}{r}=\frac{6 k-2}{3 k-1}=2$ or
$2 r-p=0$
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.