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If f(x) is a non-zero polynomial of degree four, having local extreme points at x = – 1, 0, 1; then the set S = {x ∈ R : f(x) = f(0)} contains exactly :

1. four rational numbers.
2. two irrational and two rational numbers.
3. two irrational and one rational number.
4. four irrational numbers.

Correct answer: two irrational and one rational number.

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