-6i is a root of f(x)=x^(3)-20x^(2)+ 36 x-720. Find the other roots of f(x). Write your answer as a list of simplified values separated by commas, if there is more than one value.

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-6i is a root of  f(x)=x^(3)-20x^(2)+  36 x-720. Find the other roots of  f(x). Write your answer as a list of simplified values separated by commas, if there is more than one value.

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Determine total number of roots: The number of roots is equal to the degree of the polynomial. We have: f(x) = x^3 - 20x^2 + 36x - 720 Determine the total number of roots. The degree of f(x) is 3. So, the number of roots: 3.Find conjugate of -6i: If a + bi is a root, then its conjugate a - bi is also a root of f(x). Given root: -6i Find the conjugate of -6i. The conjugate is 6i. Since complex roots come in conjugate pairs for polynomials with real coefficients, 6i is also a root of f(x).Divide by x^2 + 36: Now we have two roots: -6i and 6i. We need to find the third root. Since the polynomial is cubic, we can use synthetic division or polynomial division to divide the polynomial by (x - (-6i))(x - 6i) = (x + 6i)(x - 6i) = x^2 + 36. Divide f(x) by x^2 + 36 to find the quotient polynomial, which will be of degree 1.Perform division: Perform the division: f(x) / (x^2 + 36) = (x^3 - 20x^2 + 36x - 720) / (x^2 + 36) This division should give us a linear polynomial since we are dividing a cubic polynomial by a quadratic polynomial.Division result: The division yields: x - 20 This is because when we divide x^3 - 20x^2 + 36x - 720 by x^2 + 36, the x^3 term is canceled by x * x^2, the -20x^2 term remains unchanged, and the 36x and -720 terms are canceled by -36 * x and -36 * 20, respectively.Find third root: The linear polynomial x - 20 gives us the third root when set equal to zero: x - 20 = 0 Solving for x gives us the third root: x = 20

$-6 i$ is a root of $f(x)=x^{3}-20 x^{2}+$ $36 x-720$ . Find the other roots of $f(x)$ . $\newline$ Write your answer as a list of simplified values separated by commas, if there is more than one value.

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−6i -6 i −6i is a root of f(x)=x3−20x2+ f(x)=x^{3}-20 x^{2}+ f(x)=x3−20x2+ 36x−720 36 x-720 36x−720. Find the other roots of f(x) f(x) f(x).\newlineWrite your answer as a list of simplified values separated by commas, if there is more than one value.

$-6 i$ is a root of $f(x)=x^{3}-20 x^{2}+$ $36 x-720$ . Find the other roots of $f(x)$ . $\newline$ Write your answer as a list of simplified values separated by commas, if there is more than one value.