tmua.me Extreme Set C Paper 2 · Question 1

Let $a$ and $b$ be real constants, and define

q(x)=x^2+ax+b.

Consider the following statement.

For every real number $x$ , at least one of $q(x)$ and $q(2x)$ is strictly positive.

Which of the following correctly describes the condition $a^2<4b$ in relation to this statement?

AThe condition is necessary but not sufficient for the statement.

BThe condition is sufficient but not necessary for the statement.

CThe condition is both necessary and sufficient for the statement.

DThe condition is neither necessary nor sufficient for the statement.

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