If the graph of a polynomial touches the x-axis only at the point (5,0), which of the following statements is correct?
Answer and explanation
Correct answer: x = 5 is a zero
If the graph touches the x-axis at (5,0) then the polynomial evaluates to zero at x=5, i.e. \(p(5)=0\). Hence x=5 is a zero. "Touching" typically implies the root has even multiplicity, but the essential fact here is the value is zero. Options B and D are incorrect because the contact point has x-coordinate 5, not 0 or -5; option C is wrong because touching the axis means the polynomial is zero at that point. Exam tip: use the x-coordinate of the contact point and substitute into \(p(x)\) to verify a zero; if it only touches (doesn't cross), expect even multiplicity.
Frequently asked questions
What is the correct answer to this question?
x = 5 is a zero
Why is this the correct answer?
If the graph touches the x-axis at (5,0) then the polynomial evaluates to zero at x=5, i.e. \(p(5)=0\). Hence x=5 is a zero. "Touching" typically implies the root has even multiplicity, but the essential fact here is the value is zero. Options B and D are incorrect because the contact point has x-coordinate 5, not 0 or -5; option C is wrong because touching the axis means the polynomial is zero at that point. Exam tip: use the x-coordinate of the contact point and substitute into \(p(x)\) to verify a zero; if it only touches (doesn't cross), expect 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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