What are the solutions to the equation x^3+x^2-2x-8=0 ?

The solutions to the equation x^3+x^2-2x-8=0 are x=2,x=-3/2+i(sqrt(7))/2 ,x=-3/2-i(sqrt(7))/2

Find the zeros of x^3+x^2-2x-8=0

The zeros of x^3+x^2-2x-8=0 are x=2,x=-3/2+i(sqrt(7))/2 ,x=-3/2-i(sqrt(7))/2

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

x = 2, x = - \frac{3}{2} + i \frac{7}{2}, x = - \frac{3}{2} - i \frac{7}{2}

Solution steps

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

Factor

x^{3} + x^{2} - 2 x - 8 : (x - 2) (x^{2} + 3 x + 4)

(x - 2) (x^{2} + 3 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 3 x + 4 = 0 : x = - \frac{3}{2} + i \frac{7}{2}, x = - \frac{3}{2} - i \frac{7}{2}

The solutions are

x = 2, x = - \frac{3}{2} + i \frac{7}{2}, x = - \frac{3}{2} - i \frac{7}{2}

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

0 = x^{4} - 5 x^{2} + 4

x^{3} - 6 x^{2} + x + 28 = 0

x^{4} - 4 x^{3} + 16 x - 16 = 0

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

What are the solutions to the equation x^3+x^2-2x-8=0 ?
The solutions to the equation x^3+x^2-2x-8=0 are x=2,x=-3/2+i(sqrt(7))/2 ,x=-3/2-i(sqrt(7))/2
Find the zeros of x^3+x^2-2x-8=0
The zeros of x^3+x^2-2x-8=0 are x=2,x=-3/2+i(sqrt(7))/2 ,x=-3/2-i(sqrt(7))/2