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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $a,b,c$ are the roots of the equation
$x^3-3px^2+3qx-1=0$,
then the centroid of the triangle with vertices
$\left(a,\frac1a\right),\left(b,\frac1b\right),\left(c,\frac1c\right)$
is the point
Solution
Centroid $=\left(\dfrac{a+b+c}{3},\dfrac{\frac1a+\frac1b+\frac1c}{3}\right)$ From the equation, $a+b+c=3p$ Also $\dfrac1a+\dfrac1b+\dfrac1c=\dfrac{ab+bc+ca}{abc}=\dfrac{3q}{1}=3q$ Hence centroid $=(p,q)$ Answer: $\boxed{(p,q)}$Online Test Series, Information About Examination,
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