A student says that if the graph of a polynomial meets the y-axis at (0,0) then x=0 cannot be a zero (root) because that point lies on the y-axis. What is the correct conclusion?
Answer and explanation
Correct answer: The statement is wrong because (0,0) lies on both axes; so if the graph passes through (0,0) then \(p(0)=0\) and x=0 is a root
A root (zero) means the x-value for which the polynomial equals zero, i.e. the point has y=0. The origin (0,0) has x=0 and y=0, so if the graph passes through (0,0) then \(p(0)=0\) and x=0 is a root. Why other choices fail: A and C confuse being on the y-axis with not being a root; D is wrong because the information (0,0) is sufficient to conclude \(p(0)=0\). Exam tip: remember roots are x-values where y=0 — check coordinates to see which axis values are zero.
Frequently asked questions
What is the correct answer to this question?
The statement is wrong because (0,0) lies on both axes; so if the graph passes through (0,0) then \(p(0)=0\) and x=0 is a root
Why is this the correct answer?
A root (zero) means the x-value for which the polynomial equals zero, i.e. the point has y=0. The origin (0,0) has x=0 and y=0, so if the graph passes through (0,0) then \(p(0)=0\) and x=0 is a root. Why other choices fail: A and C confuse being on the y-axis with not being a root; D is wrong because the information (0,0) is sufficient to conclude \(p(0)=0\). Exam tip: remember roots are x-values where y=0 — check coordinates to see which axis values are zero.
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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