If `p ,q , in {1,2,3,4},` then find the number of equations of the form `p x^2+q x+1=0` having real roots.

Options

A. 15
B. 9
C. 7
D. 8

Answer

C

Explanation

The given equation will have real roots, if Discriminant `ge 0 rArr q^(2) - 4p ge 0 rArr q^(2) ge 4p`
If p = 1, then `q^(2) ge 4p rArr q^(2) ge 4 rArr q = 2, 3, 4`
p=2, then `q^(2) ge 4p rArr q^(2) ge 8 rArr q = 3, 4`
p=3, then `q^(2) ge 4p rArr q^(2) ge 12 rArr q = 4`
p = 4, then `q^(2) ge 4p rArr q^(2) ge 16 rArr q = 4`.
Thus, there are 7 cases.