If a, b in {1, 2, 3} and the equation ax^{2} | vedclass

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(C) The given quadratic equation is $ax^{2} + bx + 1 = 0$.For the equation to have real roots, the discriminant $D$ must be greater than or equal to $

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number of possible ordered pairs $(a, b)$ is $3$

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(C) The given quadratic equation is $ax^{2} + bx + 1 = 0$.For the equation to have real roots, the discriminant $D$ must be greater than or equal to $0$.$D = b^{2} - 4ac \geq 0$.Substituting $c = 1$, we get $b^{2} - 4a \geq 0$, which implies $b^{2} \geq 4a$.Given $a, b \in \{1, 2, 3\}$, we test the possible values:If $a = 1$, $b^{2} \geq 4 \implies b \in \{2, 3\}$. Pairs: $(1, 2), (1, 3)$.If $a = 2$, $b^{2} \geq 8 \implies b = 3$. Pair: $(2, 3)$.If $a = 3$, $b^{2} \geq 12 \implies$ no value of $b$ satisfies this.The possible ordered pairs $(a, b)$ are $(1, 2), (1, 3), (2, 3)$.Thus, the number of possible ordered pairs is $3$.

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

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