Question

\(f(x)\) is an \(n^{th}\) degree polynomial and \(\alpha_1,\alpha_2,\ldots,\alpha_n\) are distinct zeros of \(f(x)\). \(g(x)\) is a polynomial having three zeros common with the zeros of \(f(x)\). Assertion (A): \(|f(x)|g(x)\) is continuous and differentiable at all \(\alpha_i\).
Reason (R): \[ \lim_{x\to a}\frac{|x-a|}{x-a} \] does not exist and \[ \lim_{x\to a}|x-a|=0. \] Choose the correct option.}

• A. Both (A) and (R) are correct, (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct, (R) is not the correct explanation of (A)
• C. (A) is correct, but (R) is not correct
• D. (A) is not correct, but (R) is correct

Hint:

A function involving modulus is always continuous, but it may not be differentiable where the expression inside the modulus changes sign.

Answer 1

The Correct Option is D