What are the solutions to the equation x^4+x^3-6x^2-4x+8=0 ?

The solutions to the equation x^4+x^3-6x^2-4x+8=0 are x=1,x=-2,x=2

Find the zeros of x^4+x^3-6x^2-4x+8=0

The zeros of x^4+x^3-6x^2-4x+8=0 are x=1,x=-2,x=2

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x^{4} + x^{3} - 6 x^{2} - 4 x + 8 = 0

x = 1, x = - 2, x = 2

Solution steps

x^{4} + x^{3} - 6 x^{2} - 4 x + 8 = 0

Factor

x^{4} + x^{3} - 6 x^{2} - 4 x + 8 : (x - 1) (x + 2)^{2} (x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 2 = 0 or x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = 1, x = - 2, x = 2

x^{3} - 6 x^{2} + 1 = 0

4 x^{3} - 3 x = \frac{1}{2}

x^{4} - 16 x^{2} + 16 = 0

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

35 = (1 + x)^{4}

What are the solutions to the equation x^4+x^3-6x^2-4x+8=0 ?
The solutions to the equation x^4+x^3-6x^2-4x+8=0 are x=1,x=-2,x=2
Find the zeros of x^4+x^3-6x^2-4x+8=0
The zeros of x^4+x^3-6x^2-4x+8=0 are x=1,x=-2,x=2