What are the solutions to the equation x^3+x^2-3x-6=0 ?

The solutions to the equation x^3+x^2-3x-6=0 are x=2,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2

Find the zeros of x^3+x^2-3x-6=0

The zeros of x^3+x^2-3x-6=0 are x=2,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2

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

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

Solution steps

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

Factor

x^{3} + x^{2} - 3 x - 6 : (x - 2) (x^{2} + 3 x + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

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

(x + 1)^{4} = 0

49 x^{4} - 175 x^{2} + 144 = 0

12 x^{3} - 20 x^{2} - 5 x + 1 = 0

4 x^{4} - 125 x^{2} + 625 = 0

x^{3} + 2 x^{2} = 36 x + 72

What are the solutions to the equation x^3+x^2-3x-6=0 ?
The solutions to the equation x^3+x^2-3x-6=0 are x=2,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2
Find the zeros of x^3+x^2-3x-6=0
The zeros of x^3+x^2-3x-6=0 are x=2,x=-3/2+i(sqrt(3))/2 ,x=-3/2-i(sqrt(3))/2