What are the solutions to the equation m^3-6m^2+12m+208=0 ?

The solutions to the equation m^3-6m^2+12m+208=0 are m=-4,m=5+3sqrt(3)i,m=5-3sqrt(3)i

Find the zeros of m^3-6m^2+12m+208=0

The zeros of m^3-6m^2+12m+208=0 are m=-4,m=5+3sqrt(3)i,m=5-3sqrt(3)i

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m^{3} - 6 m^{2} + 12 m + 208 = 0

m = - 4, m = 5 + 33 i, m = 5 - 33 i

Solution steps

m^{3} - 6 m^{2} + 12 m + 208 = 0

Factor

m^{3} - 6 m^{2} + 12 m + 208 : (m + 4) (m^{2} - 10 m + 52)

(m + 4) (m^{2} - 10 m + 52) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

m + 4 = 0 or m^{2} - 10 m + 52 = 0

Solve

m + 4 = 0 : m = - 4

Solve

m^{2} - 10 m + 52 = 0 : m = 5 + 33 i, m = 5 - 33 i

The solutions are

m = - 4, m = 5 + 33 i, m = 5 - 33 i

(\frac{x \cdot 4 - 7}{3})^{3} = 27

4 x^{14} - 57 = 37

52 x^{6} = x - 23 x

51 = 4 x^{4} - 13

x^{3} - 4 x = 5

What are the solutions to the equation m^3-6m^2+12m+208=0 ?
The solutions to the equation m^3-6m^2+12m+208=0 are m=-4,m=5+3sqrt(3)i,m=5-3sqrt(3)i
Find the zeros of m^3-6m^2+12m+208=0
The zeros of m^3-6m^2+12m+208=0 are m=-4,m=5+3sqrt(3)i,m=5-3sqrt(3)i