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The Intermediate Value Theorem - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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12 Questions around this concept.
Solve by difficulty
Let $a_1<a_2<a_3<a_4$ then the number of real roots of equation $\left(x-a_1\right)\left(x-a_3\right)+\left(x-a_2\right)\left(x-a_4\right)=0$ equals
If $a_1<a_2<a_3<a_4<a_5<a_6$ then number of real roots of equation $\left(x-a_1\right)\left(x-a_3\right)\left(x-a_5\right)+\left(x-a_2\right)\left(x-a_4\right)\left(x-a_6\right)=0$ equals
If $f(x)=x^2-1$, then $f(x)=\frac{5}{4}$ has atleast ___ Solution in $[-1,2]$
Concepts Covered - 1
The Intermediate Value Theorem
The Intermediate Value Theorem (IMVT)
Let $f$ be continuous over a closed interval $[a, b]$ and $f(a) \neq f(b)$. If $z$ is any real number between $f(a)$ and $f(b)$, then there is at least one $x$ in $[a, b]$ satisfying $f(x)=z$
An important result from IMVT
If $f(x)$ is a continuous function in $[a, b]$ and $f(a)$ and $f(b)$ are of opposite signs, then there is at least one root of $f(x)$ lying in $(a, b)$.
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