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Math Help - quadratic roots

  1. #1
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    quadratic roots

    I worked out that the roots of this
    3x^2 -3

    are x=1 or x=-1 is this correct?
    my classmate said he got x=-1 or x=1.7
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  2. #2
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    Quote Originally Posted by wolfhound View Post
    I worked out that the roots of this
    3x^2 -3

    are x=1 or x=-1 is this correct?
    my classmate said he got x=-1 or x=1.7
    if you mean ...

    3x^2-3=0

    then the roots are x = \pm 1
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  3. #3
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    You are correct.

    You have 3x^2 - 3 = 0

    Divide both sides by 3

    => x^2 - 1 = 0

    Move the one to the right hand side

    => x^2 = 1 and so x = \sqrt{1} = 1 \textrm{ or } -1
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  4. #4
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    Quote Originally Posted by wolfhound View Post
    I worked out that the roots of this
    3x^2 -3

    are x=1 or x=-1 is this correct?
    my classmate said he got x=-1 or x=1.7
    You should suggest to your classmate that s/he substitute x = 1.7 into the equation and see what happens ....
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  5. #5
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    There is something of an ambiguity about the term "roots". I learned that an equation has roots while a polynomial has zeros. Specifically, the zeros of the polynomial p(x) are the roots of the equation p(x)= 0. Strictly speaking, then, you can talk about the "roots" of the equation 3x^2- 3= 0, or the "zeros" of the polynomial 3x^2- 3. But students tend to use "root" and "zero" interchangebly. In either case, since 3x^2- 3= 0 is the same as 3x^2= 3 and, dividing both sides by 3, x^2= 1, the roots are indeed x= 1 and x= -1. As mr fantastic suggested, have your friend replace x in the equation by 1.7 and see what happens. He should get approximately "6", not "0".
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  6. #6
    Senior Member Stroodle's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    There is something of an ambiguity about the term "roots". I learned that an equation has roots while a polynomial has zeros. Specifically, the zeros of the polynomial p(x) are the roots of the equation p(x)= 0. Strictly speaking, then, you can talk about the "roots" of the equation 3x^2- 3= 0, or the "zeros" of the polynomial 3x^2- 3. But students tend to use "root" and "zero" interchangebly. In either case, since 3x^2- 3= 0 is the same as 3x^2= 3 and, dividing both sides by 3, x^2= 1, the roots are indeed x= 1 and x= -1. As mr fantastic suggested, have your friend replace x in the equation by 1.7 and see what happens. He should get approximately "6", not "0".
    I was wondering about that. Thanks for the info
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