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Official 2016 Paper 2 · Q15

Paper 2Logic & proofAlgebra

Consider the quadratic f(x)=x2−2px+qf(x)=x^2-2px+q and the statement:

(*) f(x)=0f(x)=0 has two real roots whose difference is greater than 2 and less than 4.

Which one of the following statements is true if and only if (*) is true?

Aq<p2<q+4q<p^2<q+4
Bq+1<p<q+4\sqrt{q+1}<p<\sqrt{q+4}
Cq−3≤p2−4≤qq-3\leq p^2-4\leq q
Dq<p2−1<q+3q<p^2-1<q+3
Eq−2<p2−3<q+2q-2<p^2-3<q+2

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