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

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

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

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

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

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

Solution steps

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

Expand

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

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

The solutions are

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

216 = 1 r^{4 - 1}

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

27 y^{3} - 8 = 0

(49 x^{2} - 4) (x^{2} - 7) = 0

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

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