If the graph of a polynomial function intersects the y-axis at the origin (0,0), which conclusion about its zeros is correct?
Answer and explanation
Correct answer: (0) is a zero because the graph passes through the origin (0,0); hence \(p(0)=0\)
A zero (root) is an x-value a for which the function value is zero, i.e. the graph passes through (a,0). If the graph meets the y-axis at (0,0), that point lies on the x-axis as well, so \(p(0)=0\) and x=0 is a root. The closest distractor (C) is wrong because although a generic y-intercept need not be a root, the specific y-intercept here is the origin, which is also an x-intercept. Exam tip: any point of the form (a,0) on the graph immediately tells you x=a is a zero of the polynomial.
Frequently asked questions
What is the correct answer to this question?
(0) is a zero because the graph passes through the origin (0,0); hence \(p(0)=0\)
Why is this the correct answer?
A zero (root) is an x-value a for which the function value is zero, i.e. the graph passes through (a,0). If the graph meets the y-axis at (0,0), that point lies on the x-axis as well, so \(p(0)=0\) and x=0 is a root. The closest distractor (C) is wrong because although a generic y-intercept need not be a root, the specific y-intercept here is the origin, which is also an x-intercept. Exam tip: any point of the form (a,0) on the graph immediately tells you x=a is a zero of the polynomial.
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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