In which situation will 0 be a real zero of a polynomial?
Answer and explanation
Correct answer: The graph passes through (0,0)
A number a is a real zero of a polynomial p(x) if and only if \(p(a)=0\). Therefore 0 is a zero exactly when \(p(0)=0\). On the graph this means the curve must pass through the origin (0,0). The point (5,0) would indicate 5 is a zero, not 0; the point (0,5) has x=0 but y≠0 so 0 is not a root there. Exam tip: compute \(p(0)\) or check the y‑coordinate at x=0 on the graph to decide quickly.
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What is the correct answer to this question?
The graph passes through (0,0)
Why is this the correct answer?
A number a is a real zero of a polynomial p(x) if and only if \(p(a)=0\). Therefore 0 is a zero exactly when \(p(0)=0\). On the graph this means the curve must pass through the origin (0,0). The point (5,0) would indicate 5 is a zero, not 0; the point (0,5) has x=0 but y≠0 so 0 is not a root there. Exam tip: compute \(p(0)\) or check the y‑coordinate at x=0 on the graph to decide quickly.
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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