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Dennis_Churaev [7]
4 years ago
14

The complex zeros of the following polynomial function. Write f in factored form.

Mathematics
1 answer:
zavuch27 [327]4 years ago
7 0

Answer:  \bold{x=-3\qquad x=\dfrac{3+3i\sqrt3}{2}\qquad x=\dfrac{3-3i\sqrt3}{2}}

<u>Step-by-step explanation:</u>

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

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}

Answer:

x=-3\qquad x=\dfrac{3+3i\sqrt3}{2}\qquad x=\dfrac{3-3i\sqrt3}{2}

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Step-by-step explanation:

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