Question
Question: Let p, q ∈ {1, 2, 3, 4}. The number of equations of the form px<sup>2</sup> + qx + 1 = 0 having real...
Let p, q ∈ {1, 2, 3, 4}. The number of equations of the form px2 + qx + 1 = 0 having real roots is:
A
15
B
9
C
7
D
8
Answer
7
Explanation
Solution
px2 + qx + 1 = 0
D = q2 - 4p ≥ 0
If q = 1, p < 0
If q = 2, p = 1
If q = 3, p = 1, 2
If q = 4, p = 1, 2, 3, 4
Total 7 cases.