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

The solutions to the equation x^3-x^2-4=0 are x=2,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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

The zeros of x^3-x^2-4=0 are x=2,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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

x = 2, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

x = 2, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

x^{6} + 19 x^{3} - 216 = 0

x^{4} + x - 3 = 0

z^{4} + z^{2} + 1 = 0

y^{3} + 81 = 36 y

x^{3} = 6

What are the solutions to the equation x^3-x^2-4=0 ?
The solutions to the equation x^3-x^2-4=0 are x=2,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of x^3-x^2-4=0
The zeros of x^3-x^2-4=0 are x=2,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2