For a polynomial p(x) we are given p(-3)<0, p(1)=0 and p(4)>0. Which zero is certainly a root?
Answer and explanation
Correct answer: 1
p(1)=0 directly shows x=1 is a root — this is explicit. The facts p(-3)<0 and p(4)>0 only give signs of p at those x-values; they do not make -3 or 4 roots. (By continuity of polynomials, a sign change between -3 and 4 guarantees at least one root in (-3,4), but it does not identify the endpoint values as roots.) Therefore the only certain root from the given information is x=1. Exam tip: look for statements of the form p(a)=0 for a guaranteed root; sign changes indicate existence of a root in an interval, not at a specific endpoint.)
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
p(1)=0 directly shows x=1 is a root — this is explicit. The facts p(-3)<0 and p(4)>0 only give signs of p at those x-values; they do not make -3 or 4 roots. (By continuity of polynomials, a sign change between -3 and 4 guarantees at least one root in (-3,4), but it does not identify the endpoint values as roots.) Therefore the only certain root from the given information is x=1. Exam tip: look for statements of the form p(a)=0 for a guaranteed root; sign changes indicate existence of a root in an interval, not at a specific endpoint.)
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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