Question

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

• A. $15$
• B. $9$
• C. $8$
• D. $7$

Answer 1

The correct option is D $7$

To have real roots,

$D\ge 0$

$\therefore q^2-4p\ge 0$

$\therefore q^2\ge 4p$

Taking $\therefore q=4$; we have $p=1,2,3,4$

$\therefore q=3$; we have $p=1,2$

$\therefore q=2$; we have $p=1$

$\therefore q=1$; we have no value of $p$

$\therefore$ Total equation :- $4+2+1=7$