What are the solutions to the equation a^3+a^2+a=0 ?

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

Find the zeros of a^3+a^2+a=0

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

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

a = 0, a = - \frac{1}{2} + i \frac{3}{2}, a = - \frac{1}{2} - i \frac{3}{2}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a = 0 or a^{2} + a + 1 = 0

Solve

a^{2} + a + 1 = 0 : a = - \frac{1}{2} + i \frac{3}{2}, a = - \frac{1}{2} - i \frac{3}{2}

The solutions are

a = 0, a = - \frac{1}{2} + i \frac{3}{2}, a = - \frac{1}{2} - i \frac{3}{2}

x^{3} - 9 x^{2} + 26 x - 24 = 0

(x^{3} - 2)^{2} - 5 (x^{3} - 2) = 6

(x - 1)^{3} (- 1) = - 8

2 x^{3} - 6 x = 0

2 (2 x^{4} - 3 x^{2}) + 2 = - 2 x^{2} (x^{2} + 2) + x^{2} + 11

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