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

x^{3} + 3 x^{2} + 4 x + 1 = 0

x^{3} - 10 x^{2} + 37 x - 52 = 0

1000 x^{3} - 300 x^{2} + 1.5 = 0

x^{2} = 6 x^{4}

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