INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More

Content

[hide]

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

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

Equation

Roots

Algebra

But try the problem first...

Answer:2

Source

Suggested Reading

B.Stat Objective Problem 711

Challenges and Thrills of Pre-College Mathematics by University Press

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.

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIAL
Another wrong solution! The proof is wrong as it only shows that there is at least one solution. It does not show that there is exactly one solution. To complete the proof, show that the derivative of \(f(x)\) is non-negative in the interval \([0, \pi/2]\).