What are the solutions to the equation x^4-2x^3+x^2+12x+8=0 ?

The solutions to the equation x^4-2x^3+x^2+12x+8=0 are x=-1,x=2+2i,x=2-2i

Find the zeros of x^4-2x^3+x^2+12x+8=0

The zeros of x^4-2x^3+x^2+12x+8=0 are x=-1,x=2+2i,x=2-2i

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x^{4} - 2 x^{3} + x^{2} + 12 x + 8 = 0

x = - 1, x = 2 + 2 i, x = 2 - 2 i

Solution steps

x^{4} - 2 x^{3} + x^{2} + 12 x + 8 = 0

Factor

x^{4} - 2 x^{3} + x^{2} + 12 x + 8 : (x + 1)^{2} (x^{2} - 4 x + 8)

(x + 1)^{2} (x^{2} - 4 x + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - 4 x + 8 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - 4 x + 8 = 0 : x = 2 + 2 i, x = 2 - 2 i

The solutions are

x = - 1, x = 2 + 2 i, x = 2 - 2 i

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

(x^{2} - 2 x) (4 - x) = 0

x^{4} - x^{3} - 27 x + 27

6 x^{4} + 8 x^{3} = 0

2 x^{3} - 5 x^{2} + 8 x - 5

What are the solutions to the equation x^4-2x^3+x^2+12x+8=0 ?
The solutions to the equation x^4-2x^3+x^2+12x+8=0 are x=-1,x=2+2i,x=2-2i
Find the zeros of x^4-2x^3+x^2+12x+8=0
The zeros of x^4-2x^3+x^2+12x+8=0 are x=-1,x=2+2i,x=2-2i