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

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

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

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

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x - 1 = 0 : x = 1

The solutions are

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

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

2 = (1 + x)^{5}

x^{3} + x^{2} = 81 x + 81

x^{3} + 6 x^{2} + 5 x - 12 = 0

4 x^{6} 6 x^{3} = 7 x^{3}

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