# Thread: SAT II Math level 2

1. ## 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 x³ − 4x² + 2x + 4 = (x² − 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?

2. $\displaystyle y = x^3 -4x^2 +2x + 4$

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

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

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:

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

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

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