Question

Use the discriminant to determine how many real-number solutions the equation has.
36x2 - 12x + 1 = 0

How do I do this?

Answer 1

the discriminant is
b^2 - 4ac , namely the part under the √ sign of the quadratic formula

If it is positive, there are 2 different real solutions
if it is zero, there is one real answer
if it is negative, there are two complex solutions

If it is a perfect square, such as 36, there are 2 rational solutions.

so your discriminant
= 144 - 4(36)(1) = 0

mmmhhh?

Answer 2

so 36 is 6,6 so there are two solutions. Am I understanding this correctly

Answer 3

No, you aren't understanding it. The discriminant is zero, as reiuny has shown, so there is only one solution.

36x^2 - 12x + 1 = (6x -1)^2 = 0

Note that the polynomial is a perfect square. The only answer is x = 1/6