If $a, b, c \in \mathbb{R}$ and satisfy $3a + 5b + 15c = 0$,then the equation $ax^4 + bx^2 + c = 0$ has:
- Aat least one root in $(-1, 0)$
- Bat least one root in $(0, 1)$
- Cat least two roots in $(-1, 1)$
- DAll of the above
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If $f:[-5,5] \rightarrow R$ is a differentiable function and if $f^{\prime}(x)$ does not vanish anywhere,then prove that $f(-5) \neq f(5).$
Medium
View SolutionThe value of $\left[ \frac{\log (x/e)}{x - e} \right]$ for all $x > e$ is equal to (where $[.]$ denotes the greatest integer function).
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