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Y and A Tutoring Paper 2 with Answers and Hints · Q8

Paper 2Logic & proofAlgebra

Consider the following statement about the polynomial p(x)p(x) where aa and bb are real numbers with a<ba<b:

(*) There exists a number cc with a<c<ba<c<b such that p(c)=0p(c)=0.

Which of the following is true?

AThe condition p(a)p(b)<0p(a)p(b)<0 is necessary and sufficient for (*)
BThe condition p(a)p(b)<0p(a)p(b)<0 is not necessary and not sufficient for (*)
CThe condition p(a)p(b)<0p(a)p(b)<0 is necessary but not sufficient for (*)
DThe condition p(a)p(b)<0p(a)p(b)<0 is sufficient but not necessary for (*)

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