What are the solutions to the equation x^3+x^2-x-10=0 ?

The solutions to the equation x^3+x^2-x-10=0 are x=2,x=-3/2+i(sqrt(11))/2 ,x=-3/2-i(sqrt(11))/2

Find the zeros of x^3+x^2-x-10=0

The zeros of x^3+x^2-x-10=0 are x=2,x=-3/2+i(sqrt(11))/2 ,x=-3/2-i(sqrt(11))/2

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x^{3} + x^{2} - x - 10 = 0

x = 2, x = - \frac{3}{2} + i \frac{11}{2}, x = - \frac{3}{2} - i \frac{11}{2}

Solution steps

x^{3} + x^{2} - x - 10 = 0

Factor

x^{3} + x^{2} - x - 10 : (x - 2) (x^{2} + 3 x + 5)

(x - 2) (x^{2} + 3 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + 3 x + 5 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 3 x + 5 = 0 : x = - \frac{3}{2} + i \frac{11}{2}, x = - \frac{3}{2} - i \frac{11}{2}

The solutions are

x = 2, x = - \frac{3}{2} + i \frac{11}{2}, x = - \frac{3}{2} - i \frac{11}{2}

(x + 2) (2 x^{2} - 5 x) - x^{3} = 8

x, x^{3} + y^{3} + z^{3} = k^{1} - 100

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

x^{5} + 4 x^{3} = 5 x

x, (2 x^{4} \cdot y^{4} - 4 x^{2} \cdot y) = (2 x^{2} \cdot y)

What are the solutions to the equation x^3+x^2-x-10=0 ?
The solutions to the equation x^3+x^2-x-10=0 are x=2,x=-3/2+i(sqrt(11))/2 ,x=-3/2-i(sqrt(11))/2
Find the zeros of x^3+x^2-x-10=0
The zeros of x^3+x^2-x-10=0 are x=2,x=-3/2+i(sqrt(11))/2 ,x=-3/2-i(sqrt(11))/2