#### Seattle

**Valued Senior Member**

- Find all the roots, real and complex, of the equation
*x*3 – 2*x*2 + 25*x*– 50 = 0.

*x*= 2, 5*i*, –5*i*. First, factor the equation to get*x*2(*x*– 2) + 25(*x*– 2) = (*x*– 2)(*x*2 + 25) = 0. Using the multiplication property of zero, you determine that*x*– 2 = 0 and*x*= 2. You also get*x*2 + 25 = 0 and*x*2 = –25. Take the square root of each side, and

Simplify the radical, using the equivalence for*i*, and the complex solutions are

The real root is 2, and the imaginary roots are 5*i*and –5*i*.

Am I right or wrong?