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Solution


Q.

Let the function f(x)=(x2–1)|x2–ax+2|+cos|x| be not differentiable at the two points x=α=2 and x=β. Then the distance of the point (α, β) from the line 12x + 5y +10 = 0 is equal to :          [2025]
1 4  
2 3  
3 2  
4 5  

Ans.

(*)

We have, 

f(x)=(x2–1)|x2–ax+2|+cos|x|

Now, cos |x| is always differentiable

So, we will check for |x2–ax+2| and it is not differentiable at its roots.

It is given that x=α=2

⇒ (2)2–a(2)+2=0 ⇒ 4–2a+2=0 ⇒ a=3

The other root of x2–3x+2 is x=1.

Note: There is error in question, f(x) is differentiable at x = 1.