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Math Help - SAT II Math level 2

  1. #1
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    SAT II Math level 2

    Hi, my exam is nov1 n im really panicking even the easiest things dont make sense Here's the problem x − 4x + 2x + 4 = (x − 2x − 2)(x − 2)

    apparently the roots of this is supposed to be 2, 1+-the root of 3 sry cant find the symbol can u explain why?
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  2. #2
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    y = x^3 -4x^2 +2x + 4

    Finding the roots is equivalent to finding the x-intercepts of its graph and this is done by setting y = 0:

    \begin{array}{rcl}0 &  = & x^3 - 4x^2 + 2x + 4 \\ 0 & = & (x^2 - 2x -2)(x-2) \end{array}

    If the product of two integers is equal to 0, then either one or both are 0. Let's see what x values would make each factor equal to 0:

    0 = x - 2 \ \leftrightarrow \ x = 2 So one root is x = 2.

    As for the other one, it requires the quadratic formula:

    \begin{array}{rcl} 0 & = & x^2 - 2x - 2 \\  x & = & \displaystyle\frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-2)}}{2(1)} \quad \text{By the quadratic formula} \\ x & = & \displaystyle \frac{2 \pm \sqrt{12}}{2} \\ & \vdots &\end{array}

    Simplify the radical and you'll get your desired answer.
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