If the graph of a polynomial touches the x-axis at a point but does not cross it there, what does this indicate?
Answer and explanation
Correct answer: It is a zero of even multiplicity (e.g., multiplicity 2, 4, ...)
If a polynomial's graph touches the x-axis at x=a without crossing, the root at a has even multiplicity. For example, (x-a)^2 touches but does not cross. For even multiplicity the sign of f(x) on both sides of a is the same, so the curve does not pass through the axis. Option B is incorrect because an odd multiplicity root (e.g., 1 or 3) causes the graph to cross the axis. Exam tip: factor or check derivatives — if f(a)=0 and f'(a)=0 (and higher derivatives as needed), the root is likely repeated (even multiplicity).
Frequently asked questions
What is the correct answer to this question?
It is a zero of even multiplicity (e.g., multiplicity 2, 4, ...)
Why is this the correct answer?
If a polynomial's graph touches the x-axis at x=a without crossing, the root at a has even multiplicity. For example, (x-a)^2 touches but does not cross. For even multiplicity the sign of f(x) on both sides of a is the same, so the curve does not pass through the axis. Option B is incorrect because an odd multiplicity root (e.g., 1 or 3) causes the graph to cross the axis. Exam tip: factor or check derivatives — if f(a)=0 and f'(a)=0 (and higher derivatives as needed), the root is likely repeated (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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