May 10, 2020

Number of roots Problem | TOMATO B.Stat Objective 712

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Number of roots.

Number of roots - B.Stat Objective Problem


The number of roots of the equation \(xsinx=1\) in the interval \([0,{2\pi}]\) is

  • 0
  • 2
  • 53361
  • 5082

Key Concepts


Equation

Roots

Algebra

Check the Answer


Answer:2

B.Stat Objective Problem 712

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


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

Number of roots - graph

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

Final Step

or, number of roots is 2.

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