What are the solutions to the equation (x-1)^4+2(x-1)^2-3=0 ?

The solutions to the equation (x-1)^4+2(x-1)^2-3=0 are x=0,x=2,x=1+sqrt(3)i,x=1-sqrt(3)i

Find the zeros of (x-1)^4+2(x-1)^2-3=0

The zeros of (x-1)^4+2(x-1)^2-3=0 are x=0,x=2,x=1+sqrt(3)i,x=1-sqrt(3)i

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(x - 1)^{4} + 2 (x - 1)^{2} - 3 = 0

x = 0, x = 2, x = 1 + 3 i, x = 1 - 3 i

Solution steps

(x - 1)^{4} + 2 (x - 1)^{2} - 3 = 0

Expand

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 2 x + 4 = 0 : x = 1 + 3 i, x = 1 - 3 i

The solutions are

x = 0, x = 2, x = 1 + 3 i, x = 1 - 3 i

(6 x + 7)^{2} (3 x + 4) (x + 1) = 6

x^{5} - x^{4} - 3 x^{3} + 5 x^{2} - 2 x = 0

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

0.5 x^{3} - x^{2} - x + 1 = 0

m^{3} - 4 m^{2} + 6 m - 4 = 0

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