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Math Help - Why can there only be 0 to 2 answers to a quadratic equation?

  1. #1
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    Why can there only be 0 to 2 answers to a quadratic equation?

    This is one of the questions in my maths assignment which is due in a few days !.. It says.. "Why can there only be 0 to 2 answers to a quadratic equation? (Use mathematical terminology)."

    This is urgent.. please help.
    We never did quadratic equations into detail at school. I guess the teacher wants us to research ourselves, but i can't find anything about why.
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  2. #2
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    Quote Originally Posted by phillychum View Post
    This is one of the questions in my maths assignment which is due in a few days !.. It says.. "Why can there only be 0 to 2 answers to a quadratic equation? (Use mathematical terminology)."

    This is urgent.. please help.
    We never did quadratic equations into detail at school. I guess the teacher wants us to research ourselves, but i can't find anything about why.
    The quadratic equation is a second degree equation. It forms parabolas. What is the general shape of a parabola? How does this help you answer the question?

    I beg to differ in one sense though. x^2 - 1 = 0 has only one solution. (Though you can call it "two real identical" solutions for technical reasons.)

    -Dan
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  3. #3
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    The problem statement says "0 to 2 answers," which includes the case of a single root with duplicity 2.

    Remember that the "answers," which seems a poor choice of words, to a quadratic equation are also known as solutions or roots or x-intercepts.
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  4. #4
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    The equation x^2-1=0 has not only one solution...has two:-+1.the type of the quadratic that has only one solution it looks like (x-1)^2=0 or (x+1)^2=0and each solution is "double" since in this case the each graph touches the xx'axis but does not pass through to the other side.

    To study all the cases seperately you should begin from the studing of the general form of the ax^2+bx+c=0 and by taking the D=b^2-4ac

    you get *D=0 OR**D<0 OR***D>0 which means *no solution 0
    **1 one solution double ***2 two diferent solutions.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Apostolos View Post
    The equation x^2-1=0 has not only one solution...has two:-+1.
    (Ahem!) Thanks for the catch. (sheepishly wanders over to the corner muttering "My Precious!")

    -Dan
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