Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Number of roots.
The number of roots of the equation \(xsinx=1\) in the interval \([0,{2\pi}]\) is
Equation
Roots
Algebra
Answer:2
B.Stat Objective Problem 712
Challenges and Thrills of Pre-College Mathematics by University Press
\(f(x)=xsinx-1=0\)
which can be written as sinx=\(\frac{1}{x}\) and f(x) has solution at those points where sinx and \(\frac{1}{x}\) intersects
So let us draw the graph
here we see two graphs y=sin x and y=\(\frac{1}{x}\)
both graphs intersect at two points between \((0,2\pi]\)
or, number of roots is 2.
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