Answer: [tex]\bold{x=-3\qquad x=\dfrac{3+3i\sqrt3}{2}\qquad x=\dfrac{3-3i\sqrt3}{2}}[/tex]
Step-by-step explanation:
The formula for factoring a cubic is:
a³ + b³ = (a + b)(a² - ab + b²)
f(x) = x³ + 3³
= (x + 3)(x² - 3x + 9)
To find the zeros, set each factor equal to zero and solve.
0 = x + 3 0 = x² - 3x + 9
-3 = x use quadratic formula
[tex]x^2-3x+9\quad \rightarrow \quad a=1, b=-3, c=9\\\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(9)}}{2(1)}\\\\\\x=\dfrac{3\pm\sqrt{9-36}}{2}\\\\\\x=\dfrac{3\pm\sqrt{-27}}{2}\\\\\\x=\dfrac{3\pm3i\sqrt{3}}{2}[/tex]
Answer:
[tex]x=-3\qquad x=\dfrac{3+3i\sqrt3}{2}\qquad x=\dfrac{3-3i\sqrt3}{2}[/tex]
