On the graph of a function we have \(p(3)=0\) and \(p(7)=4\). Which statement is correct?
Answer and explanation
Correct answer: (3) is a zero but (7) is not
A number \(a\) is a zero (root) of a polynomial if and only if \(p(a)=0\). Here \(p(3)=0\), so 3 is a zero and the graph meets the x-axis at x=3. Since \(p(7)=4\neq0\), 7 is not a zero. Closest distractors (B and C) are wrong because they assume \(p(7)=0\). Exam tip: always check the function value equals exactly 0 before calling a point a root.
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What is the correct answer to this question?
(3) is a zero but (7) is not
Why is this the correct answer?
A number \(a\) is a zero (root) of a polynomial if and only if \(p(a)=0\). Here \(p(3)=0\), so 3 is a zero and the graph meets the x-axis at x=3. Since \(p(7)=4\neq0\), 7 is not a zero. Closest distractors (B and C) are wrong because they assume \(p(7)=0\). Exam tip: always check the function value equals exactly 0 before calling a point 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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