Final answer:
This equation can be solved using the quadratic formula. The solutions or roots of the equation x³+x=0 are ±i, where i is the imaginary unit.
Step-by-step explanation:
This equation can be solved using the quadratic formula. For an equation of the form ax²+bx+c = 0, the solutions or roots can be calculated using the formula:
x = (-b ± sqrt(b²-4ac)) / 2a
In this case, the equation is x³+x=0. Since it is in the form ax²+bx+c = 0, we can treat it as a quadratic equation. By substituting a=1, b=0, and c=1, the quadratic formula becomes:
x = (-0 ± sqrt(0²-4(1)(1)))/2(1)
Simplifying further, we get:
x = ± sqrt(-4)/2
Since the square root of a negative number is not defined in real numbers, there are no real solutions to this equation. However, in complex numbers, the solutions are:
x = ± i