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How many real roots does the polynomial x3 + 3x − 2023 have?

This question was previously asked in
CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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  2. 1
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Answer (Detailed Solution Below)

Option 2 : 1
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Detailed Solution

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Concept: 

Every odd degree polynomial p(x) ∈ R(x) has at least a real root

Explanation:

p(x) = x3 + 3x − 2023

p'(x) = 3x2 + 3

Since x2 ≥ 0 for all x so

3x2 + 3 > 0 ⇒ p'(x) > 0

Therefore p'(x) has no real roots

We know that between two distinct real roots of p(x) there exist a real root of p'(x).

Since here p'(x) no real roots, so p(x) can't have more than one real root

Option (2) correct

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