Q1. [1]
Assertion (A): The polynomial $p(x) = x^2 + 3x + 3$ has two real zeroes.
Reason (R): A quadratic polynomial can have at most two real zeroes.
Select the correct answer from the codes (a), (b), (c) and (d) as given below.
- (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- (c) Assertion (A) is true, but Reason (R) is false.
- (d) Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2023 30/2/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
(d) Assertion (A) is false, but Reason (R) is true.
For $p(x) = x^2 + 3x + 3$, discriminant $= 9 - 12 = -3 < 0$, so it has no real zeroes. Reason (R) is correct as a quadratic polynomial has at most two zeroes.
Explanation
- Check A by computing discriminant $b^2 - 4ac = 9 - 12 = -3 < 0$ → no real zeroes, so A is false.
- R is a standard result (NCERT Ch. 2, Summary point 4) → R is true.
- Since A is false and R is true, the answer is (d). Don't confuse "at most two" with "always two."
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