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by floam84 on April 3rd, 2008

floam84

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How can you determine the nature of the roots of a quadratic equation?

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  • by Anonymous on April 6th, 2008

    Anonymous

    By using the discriminant.
    If you have a quadratic equation ax^2+bx+c=0, then it is true that x=[-b±√(b^2-4ac)]/2a. That (b^2-4ac) is known as the discriminant, Δ.
    If Δ>0, then the roots are real and distinct. Further, if Δ>0 and Δ is a perfect square, then the roots are rational.
    If Δ=0, there is one solution to the quadratic equation, or two equal roots.
    If Δ<0, then the roots not real, incorporating an imaginary component.

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