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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

- 0
- 2
- 53361
- 5082

Equation

Roots

Algebra

But try the problem first...

Answer:2

Source

Suggested Reading

B.Stat Objective Problem 712

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

\(f(x)=xsinx-1=0\)

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=\(\frac{1}{x}\)

Second Hint

both graphs intersect at two points between \((0,2\pi]\)

Final Step

or, number of roots is 2.

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