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Math Help - Discriminant

  1. #1
    Junior Member
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    Discriminant

    Does the discriminant with a value of 49 indicate that the quadratic equation has (a) 2 real solutions or (b) 2 rational solutions, and why? Also, what's the difference?

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  2. #2
    MHF Contributor Mathstud28's Avatar
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    If the discriminant

    is 49 then you have two solutions because the solutions of x=\frac{-b\pm7}{2a} using the quadratic formula and as you can see you have two solutions \frac{-b+7}{2a} and \frac{-b-7}{2a}...to have only one solution you need your discriminant to be zero so the value of x that makes the polynomial zero is given by x=\frac{-b\pm0}{2a} which just gives \frac{-b}{2a} as your answer...and finally to have zero solutions you need the discriminant to be negative because your answer will be \frac{-b\pm{ic}}{2a} where i=(-1)^{\frac{1}{2}}...and since i is an imaginary number there are no REAL solutions
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