Question

If $a,b\in \{1,2,3\}$ and the equation $a{x}^2+bx+1=0$ has real roots, then

• A. $a>b$
• B. $a\le b$
• C. number of possible ordered pairs $(a,b)$ is $3$
• D. $a<b$

Answer 1

Answer: (C), (D)

The correct options are
C number of possible ordered pairs $(a,b)$ is $3$
D $a<b$

$a{x}^2+bx+1=0$
For real roots, $D\ge 0$
$b^2-4a\ge 0\Rightarrow b^2\ge 4a$
Possible pairs of $(a,b)$ are $(1,2),(1,3),(2,3)$