Q1. [1] § 2.2 Geometrical Meaning of the Zeroes of a Polynomial § 2.4 Summary
In Q. No. 19 and 20 a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
Assertion (A) : If the graph of a polynomial touches $x$-axis at only one point, then the polynomial cannot be a quadratic polynomial.
Reason (R) : A polynomial of degree $n(n > 1)$ can have at most $n$ zeroes.
- (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
- (b) Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for 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
2024 30/1/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer
(d) Assertion (A) is false but Reason (R) is true.
A quadratic polynomial can have exactly one (repeated) zero — its graph touches the x-axis at only one point (Case ii, parabola tangent to x-axis). So Assertion is false. Reason is true as a degree-$n$ polynomial has at most $n$ zeroes.
Source: Chapter 2, Section 2.2
Explanation
- Why A is false: Case (ii) in the textbook shows a parabola (quadratic) that touches the x-axis at exactly one point (two coincident/equal zeroes). So a quadratic can touch the x-axis at only one point — the assertion wrongly claims it cannot be quadratic.
- Why R is true: The textbook states a polynomial of degree $n$ has at most $n$ zeroes. This is correct.
- Since A is false and R is true, the answer is (d).
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