Final answer:
The quadratic equation 6u^(2)+24u=0 has two solutions: u = 0 and u = -4, found by factoring the equation and then solving for u.
Step-by-step explanation:
To find the roots of the quadratic equation 6u^(2)+24u=0, you can factor out the common term, which in this case is 6u. This gives you:
6u(u + 4) = 0
Setting each factor equal to zero and solving for u will give you the solutions (roots) of the equation.
- 6u = 0 implies u = 0.
- u + 4 = 0 implies u = -4.
Therefore, the two solutions to this quadratic equation are u = 0 and u = -4.