Let p, q in {1, 2, 3, 4}. The number of equat | vedclass

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(C) For the quadratic equation $px^2 + qx + 1 = 0$ to have real roots,the discriminant $D$ must be greater than or equal to $0$.$D = q^2 - 4(p)(1) \ge

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$7$

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(C) For the quadratic equation $px^2 + qx + 1 = 0$ to have real roots,the discriminant $D$ must be greater than or equal to $0$.$D = q^2 - 4(p)(1) \ge 0$$q^2 \ge 4p$Given $p, q \in \{1, 2, 3, 4\}$,we test the possible values:If $p = 1$,$q^2 \ge 4 \Rightarrow q \in \{2, 3, 4\}$ ($3$ solutions).If $p = 2$,$q^2 \ge 8 \Rightarrow q \in \{3, 4\}$ ($2$ solutions).If $p = 3$,$q^2 \ge 12 \Rightarrow q \in \{4\}$ ($1$ solution).If $p = 4$,$q^2 \ge 16 \Rightarrow q \in \{4\}$ ($1$ solution).Total number of solutions = $3 + 2 + 1 + 1 = 7$.

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

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