Let `a,b in {1,2,3}.` What is the number of equations of the form `ax^(2) + bx+ 1 = 0` having real roots?

Options

A. 1
B. 2
C. 5
D. 3

Answer

D

Explanation

The given equation is `ax^(2) + bx + 1 = 0 `
The equation has real roots.
`" When discriminant " ge 0`
`:. b^(2) - 4a ge 0`
` rArr b^(2) ge 4a`
a,b has to be selected from, three numbers , so total 3 selections are possible from, three numbers , so total 3 selections are possible when (a, b) are (1,2) , (1,3) and (2,3)
Thus the number of equations of the form `ax^(2) + bx+ 1 + 0` having real root is 3.