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

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

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

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

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

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

Solution steps

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

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

x^{5} = 2

x, 3 x^{3} + 2 y = 10

x^{3} - 15 x^{2} = 0

36 x^{4} + 29 x^{2} - 7 = 0

4 x^{3} + 16 x^{2} = 16 x + 64

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