If \(p(a)=0\) and \(p(b)=0\), where \(a\neq b\), at which points will the graph of \(p(x)\) cut the x-axis?
Answer and explanation
Correct answer: \((a,0),\ (b,0)\)
If \(p(a)=0\), the graph has y-coordinate zero at x=a, so the point is \((a,0)\); similarly \(p(b)=0\) gives \((b,0)\). Closest distractor: \((0,a)\) and \((0,b)\) would be points on the y-axis (x=0), not x-intercepts. Exam tip: a zero (root) of a polynomial is the x-value where the graph crosses the x-axis, so represent it as \((\text{root},0)\).
Frequently asked questions
What is the correct answer to this question?
\((a,0),\ (b,0)\)
Why is this the correct answer?
If \(p(a)=0\), the graph has y-coordinate zero at x=a, so the point is \((a,0)\); similarly \(p(b)=0\) gives \((b,0)\). Closest distractor: \((0,a)\) and \((0,b)\) would be points on the y-axis (x=0), not x-intercepts. Exam tip: a zero (root) of a polynomial is the x-value where the graph crosses the x-axis, so represent it as \((\text{root},0)\).
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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