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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Roots of Equation.

## Roots of Equations (B.Stat Objective Question )

The number of roots of the equation $x^2+sin^2{x}-1$ in the closed interval $[0,\frac{\pi}{2}]$ is

• 0
• 2
• 53361
• 5082

### Key Concepts

Equation

Roots

Algebra

But try the problem first…

Source

B.Stat Objective Problem 711

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

$x^2+sin^2{x}-1=0$

$\Rightarrow x^{2}=cos^{2}x$

we draw two graphs $y=x^{2} and y=cos^{2}x$

where intersecting point gives solution now we look for intersecting points

Second Hint

we get two intersecting points

Final Step

so number of roots is 2.