Let P be the statement 'the quadratic x 2 + bx + c has real roots' and Q be the statement ' c <= (b 2)/4 '. Which of the following is correct? (Here b and c are real numbers.)

P is both a necessary and a sufficient condition for Q

P is a sufficient but not a necessary condition for Q

P is neither a necessary nor a sufficient condition for Q

P is a necessary but not a sufficient condition for Q

Let $P$ be the statement 'the quadratic $x^{2} + b x + c$ has real roots' and $Q$ be the statement ' $c \leq \frac{b ^{2}}{4}$ '. Which of the following is correct? (Here $b$ and $c$ are real numbers.)

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