If \(p(-12)=0,\; p(-2)=6,\; p(4)=0,\; p(15)=0\), how many of the given x-values are zeroes (roots) of \(p\)?
Answer and explanation
Correct answer: Three
A root (zero) is an x-value where \(p(x)=0\). Here \(p(-12)=0,\; p(4)=0,\; p(15)=0\), so there are three zeros. Since \(p(-2)=6\), \(-2\) is not a zero. The closest distractor (Four) is incorrect because it would wrongly include \(-2\) despite \(p(-2)\neq0\). Exam tip: count only those x for which the function value is exactly 0 — check each given pair carefully.
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What is the correct answer to this question?
Three
Why is this the correct answer?
A root (zero) is an x-value where \(p(x)=0\). Here \(p(-12)=0,\; p(4)=0,\; p(15)=0\), so there are three zeros. Since \(p(-2)=6\), \(-2\) is not a zero. The closest distractor (Four) is incorrect because it would wrongly include \(-2\) despite \(p(-2)\neq0\). Exam tip: count only those x for which the function value is exactly 0 — check each given pair carefully.
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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