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May 9, 2020

Roots of Equation | TOMATO B.Stat Objective 711

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

Check the Answer


Answer:2

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.

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One comment on “Roots of Equation | TOMATO B.Stat Objective 711”

  1. 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 \([0, \pi/2]\).

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