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

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Solution

The correct option is C 7
For real roots, discriminant $\geq 0$
$\Rightarrow q^{2} - 4 p \geq 0 \Rightarrow q^{2} \geq 4 p$
For $p = 1, q^{2} \geq 4 \Rightarrow q = 2, 3, 4$
$p = 2, q^{2} \geq 8 \Rightarrow q = 3, 4$
$p = 3, q^{2} \geq 12 \Rightarrow q = 4$
$p = 4, q^{2} \geq 16 \Rightarrow q = 4$
Total seven solutions are possible

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