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
Equation
Roots
Algebra
Answer:2
B.Stat Objective Problem 711
Challenges and Thrills of Pre-College Mathematics by University Press
\(x^2+sin^2{x}-1=0\)
\(\Rightarrow x^{2}=cos^{2}x\)
we draw two graphs \(y=x^{2} and y=cos^{2}x\)
where intersecting point gives solution now we look for intersecting points
we get two intersecting points
so number of roots is 2.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.
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 \([0, \pi/2]\).