Question

Find the values of 'p' for which the quadratic equation ${px}^2+4x+1=0$ has real roots.

• A. $p\le 4$
• B. $p\ge 6$
• C. $p\ge 4$
• D. None of these

Answer 1

Answer: (A)

$p\le 4$

Given equation is: $p{x}^2+4x+1=0$

$\therefore a=p,b=4,c=1$

For real roots $D\ge 0$, $b^2-4ac\ge 0$
$\Rightarrow {\left(4\right)}^2-4.p.1\ge 0$
$\Rightarrow 16\ge 4p$
$\Rightarrow 4p\le 16$
$\Rightarrow p\le 4$