If the graph of a polynomial function y = p(x) passes through the point (0,0) on the y-axis, which conclusion about its zeroes is correct?
Answer and explanation
Correct answer: \(x=0\) is a zero because \(p(0)=0\)
The point (0,0) means that when \(x=0\), \(y=p(0)=0\). Roots of a polynomial are the x-values for which \(p(x)=0\). Hence \(x=0\) is indeed a root. The closest distractor is C — claiming it is only a y-intercept — which is incorrect here because (0,0) lies on the x-axis as well, so it gives an x-intercept. Exam tip: substitute the x-coordinate of the given point into \(p(x)\); if it yields zero, that x is a root.
Frequently asked questions
What is the correct answer to this question?
\(x=0\) is a zero because \(p(0)=0\)
Why is this the correct answer?
The point (0,0) means that when \(x=0\), \(y=p(0)=0\). Roots of a polynomial are the x-values for which \(p(x)=0\). Hence \(x=0\) is indeed a root. The closest distractor is C — claiming it is only a y-intercept — which is incorrect here because (0,0) lies on the x-axis as well, so it gives an x-intercept. Exam tip: substitute the x-coordinate of the given point into \(p(x)\); if it yields zero, that x is a root.
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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