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Let $\mathrm{a}, \mathrm{b} \in\{1,2,3\}$. What is the number of equations
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The correct answer is:
3
The given equation is $a x^{2}+b x+1=0$ This equation has real roots When discriminant $\geq 0$ $b^{2}-4 a \geq 0$
$\Rightarrow b^{2} \geq 4 a$
$\mathrm{a}, \mathrm{b}$ has to be selected from, three numbers, so total selections are possible when $(\mathrm{a}, \mathrm{b})$ are $(1,2),(1,3)$ and
$(2,3) .$
Thus, the number of equations of the form $a x^{2}$ $\mathrm{bx}+1=0$ having real root is 3
$\Rightarrow b^{2} \geq 4 a$
$\mathrm{a}, \mathrm{b}$ has to be selected from, three numbers, so total selections are possible when $(\mathrm{a}, \mathrm{b})$ are $(1,2),(1,3)$ and
$(2,3) .$
Thus, the number of equations of the form $a x^{2}$ $\mathrm{bx}+1=0$ having real root is 3
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