QJEEM25Ma9a9c: JEE Main 2025 Mathematics - Class 12 JEEM25Ma9a9c Solution: Let the function be not differentiable at the two points and .…

Question

Verified Solution • 2025–26 Session moderate

Let the function

f(x)=\left(x^2-1\right)\left|x^2-a x+2\right|+\cos |x|

be not differentiable at the two points

x=\alpha=2

and

x=\beta

. Then the distance of the point

(\alpha, \beta)

from the line

12 x+5 y+10=0

is equal to :

Accepted Answer

$\cos |\mathrm{x}|$ is always differentiable

$\therefore$ we have to check only for $\left|\mathrm{x}^2-\mathrm{ax}+2\right|$

$\therefore$ Not differentiable at

$x^{2} - a x + 2 = 0$

One root is given, $\alpha=2$

$\begin{aligned} ∴ 4 & - 2 a + 2 = 0 \\ a = 3 \end{aligned}$

$\therefore$ other root $\beta=1$

but for $x=1 f(x)$ is differentiable

(Drop)

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