tmua.me Medium Set A Paper 2 · Question 4

Let $f(x)=x^2+px+q$ , where $p$ and $q$ are real constants, and suppose that $f(x)=0$ has two distinct real roots. Consider the statements

\begin{array}{ll}P:& f(1)>0,\\[3pt]Q:&\text{both roots of }f(x)=0\text{ are greater than }1.\end{array}

Which of the following is true?

P

is sufficient but not necessary for

Q

P

is both necessary and sufficient for

Q

P

is neither necessary nor sufficient for

Q

P

is necessary but not sufficient for

Q

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