Suppose f(x) is a polynomial of degree four

Question:

Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1,0,1$. If $T=\{x \in \mathbf{R} \mid f(x)=f(0)\}$, then the sum of squares of all the elements of $T$ is :

  1. (1) 4

  2. (2) 6

  3. (3) 2

  4. (4) 8


Correct Option: 1

Solution:

$\because$ The critical points are $-1,0,1$

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