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March 28, 2017

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use the discriminant to determine whether the following equations have solutions that are: tow different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. 25x^2=10x-1

  • Pre Algebra - ,

    25x^2 - 10x + 1 = 0

    discriminant = b^2 - 4ac = 100-100 = 0

    so, the roots are the same.

    (5x-1)(5x-1)

    Why does the discriminant determine how many roots? Well, the roots are basically -b/2a +/- the discriminant. So, if the discriminant is zero, both roots are -b/2a

    If the discriminant is positive, both roots are the same distance away from -b/2a

    If the discriminant is negative, there is no real square root, and we have complex roots.

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