What are the solutions to the equation x^3+x^2-12=0 ?

The solutions to the equation x^3+x^2-12=0 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

Find the zeros of x^3+x^2-12=0

The zeros of x^3+x^2-12=0 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

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x^{3} + x^{2} - 12 = 0

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

Solution steps

x^{3} + x^{2} - 12 = 0

Factor

x^{3} + x^{2} - 12 : (x - 2) (x^{2} + 3 x + 6)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 3 x + 6 = 0 : x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

The solutions are

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

x^{4} + 4 x^{3} - 1 = 0

s^{5} + s^{4} + 4 s^{3} + 24 s^{2} + 3 s + 63 = 0

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x = 0

x^{3} - 7 x + 2 = 0

3 x^{4} - 7 x^{3} - 9 x^{2} + 24 x - 4

What are the solutions to the equation x^3+x^2-12=0 ?
The solutions to the equation x^3+x^2-12=0 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2
Find the zeros of x^3+x^2-12=0
The zeros of x^3+x^2-12=0 are x=2,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2