Algebra HELP:(

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

How do I do this?

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  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?

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

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  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

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