If the graph of a polynomial touches the x-axis at the single point (m, 0) and does not meet the x-axis anywhere else, how many distinct real zeros does the polynomial have?
Answer and explanation
Correct answer: One
A touch at (m,0) means the polynomial satisfies \(p(m)=0\). If the graph only touches and does not cross the x-axis at that point, the root at x = m has even multiplicity (2, 4, ...). Regardless of that multiplicity, it represents a single distinct real zero — x = m. The distractor 'two' is incorrect because two distinct real zeros would require the graph to meet the x-axis at two different x-values. Exam tip: check \(p(m)=0\) and use root multiplicity (even → touch, odd → cross) to decide crossing vs touching.
Frequently asked questions
What is the correct answer to this question?
One
Why is this the correct answer?
A touch at (m,0) means the polynomial satisfies \(p(m)=0\). If the graph only touches and does not cross the x-axis at that point, the root at x = m has even multiplicity (2, 4, ...). Regardless of that multiplicity, it represents a single distinct real zero — x = m. The distractor 'two' is incorrect because two distinct real zeros would require the graph to meet the x-axis at two different x-values. Exam tip: check \(p(m)=0\) and use root multiplicity (even → touch, odd → cross) to decide crossing vs touching.
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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