Simplifying Complex Expressions|Please Help!

Question

1. Use the quadratic formula to help identify the x-intercepts of the function f(x) = -x² + 2x - 2. Write each solution in the form of x = a + bi.
2. Use the quadratic formula to help identify the x-intercepts of the function f(x) = 2x² - 2x + 1. Write each solution in the form of x = a + bi.

Answer 1

If Ax² + Bx + C = 0, then x = [-B ± √(B² - 4AC)] / (2A).

So, if 2x² - 2x + 1 = 0, then x = [2 ± √(4 - 8)] / 4 = [2 ± √(-4)] / 4 = [2 ± 2i] / 4 = (2/4) ± (2/4)i = (1/2) ± (1/2)i

x = (1/2) + (1/2)i or (1/2) - (1/2)i

Do the other problem in a similar manner.

Answer 2

The quadratic formula is:

x = (-b/2a) ± √(b²-4ac) / 2a

You can also look the formula up in your textbook or on-line. For the equation f(x) = -x² + 2x - 2, a = -1, b= 2, c = -2. Plug the numbers into the quadratic formula and compute the answers. You'll get two.