If p,q∈{1,2,3,4}, the number of equations of the form px2+qx+1=0 having real roots is
7
8
15
9
For real roots, we must have
Disc ≥0⇒q2−4p≥0⇒q2≥4p If p=1, then q2≥4p⇒q2≥4⇒q=2,3,4p=2, then q2≥4p⇒q2≥8⇒q=3,4p=3, then q2≥4p⇒q2≥12⇒q=4p=4, then q2≥4p⇒q2≥16⇒q=4
Thus, we see that there are 7 cases.