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Math Help - Need some help to prove Discriminant in a part of the quadratic equation

  1. #1
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    Question Need some help to prove Discriminant in a part of the quadratic equation

    Hello

    Im kinda stuck in a step to reshape a formula that is a part of quadratic equation:

    Need some help to prove Discriminant in a part of the quadratic equation-equation.png

    I hope someone can give me a step by step of how its done.
    Thank you very much!
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  2. #2
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    Re: Need some help to prove Discriminant in a part of the quadratic equation

    hi
    Attached Thumbnails Attached Thumbnails Need some help to prove Discriminant in a part of the quadratic equation-6666666666666666.jpg  
    Thanks from Assassinbeast
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  3. #3
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    Re: Need some help to prove Discriminant in a part of the quadratic equation

    Quote Originally Posted by Assassinbeast View Post
    Click image for larger version. 

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    I hope someone can give me a step by step of how its done.

    I do not fully understand your need,

    But from what you have posted:
    {\left( {x + \frac{b}{{2}}} \right)^2} = \frac{{b^2}}{{4}}

    Now what?
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    Re: Need some help to prove Discriminant in a part of the quadratic equation

    Thank you abualabed, i got it now
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    Re: Need some help to prove Discriminant in a part of the quadratic equation

    Quote Originally Posted by Plato View Post
    I do not fully understand your need,

    But from what you have posted:
    {\left( {x + \frac{b}{{2}}} \right)^2} = \frac{{b^2}}{{4}}

    Now what?
    It was just those two steps that i posted that i needed to know
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  6. #6
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    Re: Need some help to prove Discriminant in a part of the quadratic equation

    For any number, a, (x+ a)^2= x^2+ 2ax+ a^2. Comparing that to x^2+ bx we see that we need 2a= b so that a= b/2 and then a^2= \frac{b^2}{4}. To make that a perfect square, we need to add \frac{b^2}{4} and, of course, subtract it:
    x^2+ bx= x^2+ bx+ \frac{b^2}{4}- \frac{b^2}{4}= \left(x- \frac{b}{2}\right)^2- \frac{b^2}{4}
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