Question

Let p,q $\in$ {1,2,3,4}. The number of equation of the form $p{x}^2+qx+1=0$ having real roots is

• A. 15
• B. 9
• C. 7
• D. 8

Answer 1

The correct option is C 7

For real roots, discriminant $\ge 0$
$\Rightarrow q^2-4p\ge 0\Rightarrow q^2\ge 4p$
For $p=1,q^2\ge 4\Rightarrow q=2,3,4$
$p=2,q^2\ge 8\Rightarrow q=3,4$
$p=3,q^2\ge 12\Rightarrow q=4$
$p=4,q^2\ge 16\Rightarrow q=4$
Total seven solutions are possible