What are the solutions to the equation a^3+(1-a)^2-1=0 ?

The solutions to the equation a^3+(1-a)^2-1=0 are a=0,a=1,a=-2

Find the zeros of a^3+(1-a)^2-1=0

The zeros of a^3+(1-a)^2-1=0 are a=0,a=1,a=-2

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

a = 0, a = 1, a = - 2

Solution steps

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

Expand

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

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

Factor

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

a (a - 1) (a + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a = 0 or a - 1 = 0 or a + 2 = 0

Solve

a - 1 = 0 : a = 1

Solve

a + 2 = 0 : a = - 2

The solutions are

a = 0, a = 1, a = - 2

x^{3} - 2 x^{4} = 13

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

x^{3} + 5 x^{2} - 8 x - 20 = 0

x^{5} + 5 = 3 x^{4} + x

(x + 1)^{3} - 6 (x + 1) - 4 = 0

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