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  4. If a, b ∈(1, 2, 3) and the equation ax2 + bx + 1 = 0 has real roots, then

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Q. If $a, b\,\in\left(1, 2, 3\right)$ and the equation $ax^2 + bx + 1 = 0$ has real roots, then

WBJEEWBJEE 2017Complex Numbers and Quadratic Equations

Solution:

We have,
$a x^{2}+b x+1=0$
For real roots, $D \geq 0$
$\therefore {b}^{2}-4 a \geq 0 $
$\Rightarrow b^{2} \geq 4 a $
$\therefore (a, b)=(1,2),(1,3),(2,3)$
$\therefore $ Number of ordered pairs $(a, b)=3$
and $a$ is always less than $b$.