Answer:
[tex]x=-4,\dfrac{1\pm\sqrt{11}i}{2}[/tex]
Step-by-step explanation:
The synthetic division shown below both confirms that x=-4 is a solution and gives the reduced quadratic as
x^2 -x +3 = 0
Using the quadratic formula with a=1, b=-1, c=3, we find the other two solutions to be ...
[tex]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(3)}}{2(1)}=\dfrac{1\pm\sqrt{-11}}{2}\\\\x=\dfrac{1\pm\sqrt{11}i}{2}[/tex]
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The graph of the cubic shows it has one real root at x=-4. Dividing the function by the corresponding factor shows the quadratic factor to have its vertex at (0.5, 2.75). This means the remaining roots are 0.5±i√2.75, matching the above result.
