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Math Help - quadratic formula problem

  1. #1
    echidnajess
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    quadratic formula problem

    Hi, I'm actually in a college precal2 class, but I think this is an alegbra issue...

    I'm sure I'm just being an idiot and doing something completely stupid here, as I haven't taken a math class in over a year and have forgotten everything, but this is my problem:

    When working on factoring something for a rational function problem, I can't seem to get the quadratic formula to work out properly.

    ex. f(x)= -x^2 - x + 6

    y= ( 1 +or- sqrt( -1^2 - 4(-1)(6) ) / 2(=1)
    solving this gets me y= -3 or 2

    which means the factors are (x+3)(x-2), right? But then multiplying those back together gets x^2 + x - 6, which is the same as the start, but with all the signs flipped... am I suppposed to be putting a negative out front, like -(x+3)(x-2)? I'm really confused... does this also mean that if the original function was something like 2x^2 - x +6, I'd need to put a 2 somewhere? I don't get it, and can't remember what I'm supposed to do...

    I'm sure this is just a stupid simple mistake, but I'd really like some help, I'm just frustrating myself at the moment.... Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by echidnajess View Post
    Hi, I'm actually in a college precal2 class, but I think this is an alegbra issue...

    I'm sure I'm just being an idiot and doing something completely stupid here, as I haven't taken a math class in over a year and have forgotten everything, but this is my problem:

    When working on factoring something for a rational function problem, I can't seem to get the quadratic formula to work out properly.

    ex. f(x)= -x^2 - x + 6

    y= ( 1 +or- sqrt( -1^2 - 4(-1)(6) ) / 2(=1)
    solving this gets me y= -3 or 2

    which means the factors are (x+3)(x-2), right? But then multiplying those back together gets x^2 + x - 6, which is the same as the start, but with all the signs flipped... am I suppposed to be putting a negative out front, like -(x+3)(x-2)? I'm really confused... does this also mean that if the original function was something like 2x^2 - x +6, I'd need to put a 2 somewhere? I don't get it, and can't remember what I'm supposed to do...

    I'm sure this is just a stupid simple mistake, but I'd really like some help, I'm just frustrating myself at the moment.... Thanks!
    <br />
f(x)= a~x^2 + b~ x + c<br />

    quadratic formula:

    <br />
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}<br />

    In your case a=-1,\ b=-1,\ c=6, so the roots are:

    <br />
x=\frac{1 \pm \sqrt{(-1)^2-4(-1)6}}{2(-1)}= \frac{1 \pm \sqrt{1+24}}{-2}=-3, 2<br />

    Now if we form (x+3)(x-2) the coefficient of x^2 is 1 so to get the original form back we always have to multiply through by the coefficient of x^2. In this case to get:

    <br />
f(x)= -x^2 - x + 6=-(x+3)(x-2)<br />

    RonL
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  3. #3
    MHF Contributor
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    Quote Originally Posted by echidnajess View Post
    Hi, I'm actually in a college precal2 class, but I think this is an alegbra issue...

    I'm sure I'm just being an idiot and doing something completely stupid here, as I haven't taken a math class in over a year and have forgotten everything, but this is my problem:

    When working on factoring something for a rational function problem, I can't seem to get the quadratic formula to work out properly.

    ex. f(x)= -x^2 - x + 6

    y= ( 1 +or- sqrt( -1^2 - 4(-1)(6) ) / 2(=1)
    solving this gets me y= -3 or 2

    which means the factors are (x+3)(x-2), right? But then multiplying those back together gets x^2 + x - 6, which is the same as the start, but with all the signs flipped... am I suppposed to be putting a negative out front, like -(x+3)(x-2)? I'm really confused... does this also mean that if the original function was something like 2x^2 - x +6, I'd need to put a 2 somewhere? I don't get it, and can't remember what I'm supposed to do...

    I'm sure this is just a stupid simple mistake, but I'd really like some help, I'm just frustrating myself at the moment.... Thanks!
    f(x) = -x^2 -x +6
    is the function of x only.
    It's graph is a parabola that opens downward.
    That's all.

    If you want to get the factors of f(x) = -x^2 -x +6, you cannot.
    But you can get its zeroes.
    Meaning, the values of x when f(x) = 0.

    When f(x) = 0, you can now factor that.
    So,
    0 = -x^2 -x +6
    That's when you can use the Quadrtatic Formula to find the x's when f(x) = 0.
    That's when you find the factors too.

    Now,
    0 = -x^2 -x +6 ------------(1)
    Transpose all of those in the righthand side of the equation to the lefthand side, and transpose the zero to the righthand side,
    x^2 +x -6 = 0 ------------(2)

    Whoa, (1) became (2)?
    So, (2) = (1) ?

    Yes, it is.

    Again,
    0 = -x^2 -x +6
    Divide both sides by -1,
    0 = x^2 +x -6

    Eh?

    What about this:
    2x^2 +6x +34 = 0 -------------(3)
    Divide both sides by 2,
    x^2 +3x +17 = 0 -------------(4)
    Are (3) and (4) equal?
    Try graphing them.

    ------------------------------------------
    Edit:

    If you want to get the factors of f(x) = -x^2 -x +6, you cannot.

    I'd be crucified for that blasphemy.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ticbol View Post
    ------------------------------------------
    Edit:

    If you want to get the factors of f(x) = -x^2 -x +6, you cannot.

    I'd be crucified for that blasphemy.
    f(x) = -x^2 -x +6 = (-x-3)(x-2)

    RonL
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