What are the solutions to the equation factor x^4+x^3+x^2=0 ?

The solutions to the equation factor x^4+x^3+x^2=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

Find the zeros of factor x^4+x^3+x^2=0

The zeros of factor x^4+x^3+x^2=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2

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factor

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

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

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

p^{4} - 4 p + 3 = 0

x^{3} - 6 x^{2} + 9 x - 3 = 0

(x^{2} + 9)^{2} = 0

4 x^{3} - 8 x^{2} - 25 x + 50 = 0

4 x^{3} + 12 x^{2} + 9 x = 0

What are the solutions to the equation factor x^4+x^3+x^2=0 ?
The solutions to the equation factor x^4+x^3+x^2=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2
Find the zeros of factor x^4+x^3+x^2=0
The zeros of factor x^4+x^3+x^2=0 are x=0,x=-1/2+i(sqrt(3))/2 ,x=-1/2-i(sqrt(3))/2