If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax $2$

+ bx + 1 = 0 having real roots is

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answer is C.

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Detailed Solution

Given, roots are real, a and b can take values 1,2,3,4.

a x 2 + b x + 1 = 0

We know that for real or equal roots,
Discriminant(D) >=0 then

b 2 > = 4 a c

⇒

b 2 > = 4 a (c = 1)

If b=2, a can 1 .......(Possibility 1)
If b=3, a can 2 .......(Possibility 2)
If b=3, a can 1 .......(Possibility 3)
If b=4, a can 2 .......(Possibility 4)
If b=4, a can 3 .......(Possibility 5)
If b=4, a can 1 .......(Possibility 6)
Thus, there can be 6 equations of the required form.
So, the correct option is 3.

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