Which of the following graphs will have exactly one real zero?
Answer and explanation
Correct answer: One that touches the x-axis at only one point (tangent)
A zero corresponds to an x-value where the graph meets the x-axis. If a graph touches the x-axis at exactly one point (is tangent there), that x-location is a single real zero — although the root may have multiplicity >1, it still gives only one distinct real solution, so B is correct. Option A gives two distinct intersections → two real zeros. Option C never meets the x-axis → no real zeros. Option D (graph coincides with the x-axis) yields infinitely many zeros. Exam tip: check whether the graph crosses the x-axis (gives distinct zeros) or merely touches it (gives one distinct zero with even multiplicity).
Frequently asked questions
What is the correct answer to this question?
One that touches the x-axis at only one point (tangent)
Why is this the correct answer?
A zero corresponds to an x-value where the graph meets the x-axis. If a graph touches the x-axis at exactly one point (is tangent there), that x-location is a single real zero — although the root may have multiplicity >1, it still gives only one distinct real solution, so B is correct. Option A gives two distinct intersections → two real zeros. Option C never meets the x-axis → no real zeros. Option D (graph coincides with the x-axis) yields infinitely many zeros. Exam tip: check whether the graph crosses the x-axis (gives distinct zeros) or merely touches it (gives one distinct zero with even multiplicity).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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