What are the solutions to the equation m(m-1)(m-2)-6=0 ?

The solutions to the equation m(m-1)(m-2)-6=0 are m=3,m=sqrt(2)i,m=-sqrt(2)i

Find the zeros of m(m-1)(m-2)-6=0

The zeros of m(m-1)(m-2)-6=0 are m=3,m=sqrt(2)i,m=-sqrt(2)i

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m (m - 1) (m - 2) - 6 = 0

m = 3, m = 2 i, m = - 2 i

Solution steps

m (m - 1) (m - 2) - 6 = 0

Expand

m (m - 1) (m - 2) - 6 : m^{3} - 3 m^{2} + 2 m - 6

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

Factor

m^{3} - 3 m^{2} + 2 m - 6 : (m - 3) (m^{2} + 2)

(m - 3) (m^{2} + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

m - 3 = 0 or m^{2} + 2 = 0

Solve

m - 3 = 0 : m = 3

Solve

m^{2} + 2 = 0 : m = 2 i, m = - 2 i

The solutions are

m = 3, m = 2 i, m = - 2 i

7 x^{6} = - 15

x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 3 = 0

3 x^{3} + 18 x^{2} + 10 x = - 5 x

x^{3} - 6 x^{2} - 36 x + 216 = 0

n^{3} - n = 8 n^{2} - 8

What are the solutions to the equation m(m-1)(m-2)-6=0 ?
The solutions to the equation m(m-1)(m-2)-6=0 are m=3,m=sqrt(2)i,m=-sqrt(2)i
Find the zeros of m(m-1)(m-2)-6=0
The zeros of m(m-1)(m-2)-6=0 are m=3,m=sqrt(2)i,m=-sqrt(2)i