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b2 - 4ac = 0 can someone briefly explain thanks

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    This buisness about equal roots etc, when in a C1 question you need to show a proof by uising b2 - 4ac = 0 or greater, or not greater, what does that mean? so for example, when does it show it has equal roots, what does it mean when its smaller than zero etc?

    thanks.
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    b²-4ac < 0. Look at the formula. You can't take the square root of a negative number so this means there are no real roots (and the quadratic doesn't cross the x axis).

    b²-4ac = 0. The roots are equal. The curve just touches the x axis at 1 point.

    b²-4ac > 0. You can take the + or - square root so there are 2 real roots.
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    Are you familiar with the quadratic formula?

    The roots of the equation ax²+bx+c are given by:
    x = {-b ± sqrt[b²-4ac]}/2a

    If b²-4ac=0, then x=-b/2a, i.e. one root.
    If b²-4ac>0, then x=(-b ± k)/2a, i.e. two roots.
    If b²-4ac<0, you'd take the square root of a negative number, so no real roots exist.
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    (Original post by LondonBoy)
    This buisness about equal roots etc, when in a C1 question you need to show a proof by uising b2 - 4ac = 0 or greater, or not greater, what does that mean? so for example, when does it show it has equal roots, what does it mean when its smaller than zero etc?

    thanks.
    If you think about the quadratic formula for the solutions of

    ax^2 + bx+c=0

    you'll see that the roots are

    (i) repeated/equal if b^2 - 4ac =0
    (ii) distinct if b^2 - 4ac >0
    (iii) complex and conjugate (or there are no real roots) if b^2 - 4ac <0, because here is a negative number you can't take the square root of (unless you have knowledge of complex numbers).
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    (Original post by LondonBoy)
    This buisness about equal roots etc, when in a C1 question you need to show a proof by uising b2 - 4ac = 0 or greater, or not greater, what does that mean? so for example, when does it show it has equal roots, what does it mean when its smaller than zero etc?

    thanks.


    the equation has one root what it equals to zero coz :
    x = [-b +- sqrt(b^2 - 4 a c ) ] / 2a
    the sqrt of (b^2 -4ac) might be positive or negative if it was more than 0 , e.g. sqrt(9) = +/- 3
    sqrt (4) = +/- 2
    but sqrt (0) = 0
    so there is only 1 value of x
    when b^2 - 4 a c is less tahn 0, then it has no real sqrt, so there is no real value for x
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    It's busy on here tonight.
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    (Original post by LondonBoy)
    This buisness about equal roots etc, when in a C1 question you need to show a proof by uising b2 - 4ac = 0 or greater, or not greater, what does that mean? so for example, when does it show it has equal roots, what does it mean when its smaller than zero etc?

    thanks.


    u r so lucky, u got the answe from 4 different ppl, in 4 different ways!!
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    Thanks - pure legends!
Updated: February 20, 2005
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