Which of the following expressions is NOT equivalent to LaTeX: x^4+6x^2+8 (x^2+2)(x+2i)(x-2i)
(x+2i)(x-2i)(x+sqrt2i)(x-sqrt2i)
(x+2i)(x-2i)(x^2+4)
(x^2+4)(x+sqrt2i)(x-sqrt2i)

(x^2+4)(x+sqrt2i)(x-sqrt2i)

Step-by-step explanation:

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.

Find all the roots, real and imaginary, of the equation 5x2 – 8x + 5 = 0.

x = 0.4 + 0.6i, 0.4 – 0.6i. The quadratic doesn’t factor, so you use the quadratic formula:

The only two solutions are complex: 0.4 + 0.6i and 0.4 – 0.6i.