What are the solutions to the equation x^4-4x^3+4x^2-36x-45=0 ?

The solutions to the equation x^4-4x^3+4x^2-36x-45=0 are x=-1,x=5,x=3i,x=-3i

Find the zeros of x^4-4x^3+4x^2-36x-45=0

The zeros of x^4-4x^3+4x^2-36x-45=0 are x=-1,x=5,x=3i,x=-3i

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x^{4} - 4 x^{3} + 4 x^{2} - 36 x - 45 = 0

x = - 1, x = 5, x = 3 i, x = - 3 i

Solution steps

x^{4} - 4 x^{3} + 4 x^{2} - 36 x - 45 = 0

Factor

x^{4} - 4 x^{3} + 4 x^{2} - 36 x - 45 : (x + 1) (x - 5) (x^{2} + 9)

(x + 1) (x - 5) (x^{2} + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 5 = 0 or x^{2} + 9 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 5 = 0 : x = 5

Solve

x^{2} + 9 = 0 : x = 3 i, x = - 3 i

The solutions are

x = - 1, x = 5, x = 3 i, x = - 3 i

12 x^{3} - 6 x^{2} = 0

x^{3} - 9 x^{2} + 31 x - 39

4 x^{3} - 18 x^{2} + 24 x = 0

x^{3} - 2 - 2 \times i = 0

4 x^{3} - 57 x^{2} + 252 x - 324 = 0

What are the solutions to the equation x^4-4x^3+4x^2-36x-45=0 ?
The solutions to the equation x^4-4x^3+4x^2-36x-45=0 are x=-1,x=5,x=3i,x=-3i
Find the zeros of x^4-4x^3+4x^2-36x-45=0
The zeros of x^4-4x^3+4x^2-36x-45=0 are x=-1,x=5,x=3i,x=-3i