Question

The values of $P$ for which the given quadratic equation has real roots, $P{x}^2+4x+1=0$ is:

• A. $P<4$
• B. $P\le 4$
• C. $P>4$
• D. $P\ge 4$

Answer 1

The correct option is B $P\le 4$

For real roots, $D\ge 0$

$b^2-4ac\ge 0$
In the given equation, $a=P$, $b=4$ and $c=1$
$b^2-4ac=\left(4^2\right)-4P\times 1\ge 0$
$16-4P\ge 0$
$4P\le 16$
$P\le 4$