Seattle
Valued Senior Member
- Find all the roots, real and complex, of the equation x3 – 2x2 + 25x – 50 = 0.
x= 2, 5i, –5i. First, factor the equation to get x2(x – 2) + 25(x – 2) = (x – 2)(x2 + 25) = 0. Using the multiplication property of zero, you determine that x – 2 = 0 and x = 2. You also get x2 + 25 = 0 and x2 = –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 5i and –5i.
Am I right or wrong?