Question

What are the solutions of x-2x + 2 = 0?

A. x=1+i or x = 1- i
B. X = 2+i or x = 2 - 1
C. x = 21 or x = -21
D. x = i or x= -1

Answer 1

The equation given by the student has a typo. Assuming the correct equation is x² - 2x + 2 = 0, the quadratic formula gives two complex solutions: 1 + i and 1 - i. Hence, option A is correct.

Step-by-step explanation:

The student has provided the equation x-2x + 2 = 0, which appears to have a typographical error. The correct format of a quadratic equation should be in the form ax² + bx + c = 0. Assuming the equation was meant to be x² - 2x + 2 = 0, we can solve this using the quadratic formula, which is x = (-b ± √(b² - 4ac))/(2a). Plugging the coefficients from the equation into the formula (where a = 1, b = -2, and c = 2), we get two possible solutions for x.

Using the given formula:

1. Calculate the discriminant: D = b² - 4ac
2. Calculate the two possible values for x: x = (-b + √D) / (2a) and x = (-b - √D) / (2a)

For the equation x² - 2x + 2 = 0, the discriminant is (-2)² - 4(1)(2) = 4 - 8 = -4, which is less than zero. This indicates the solutions will be complex numbers.

Therefore, the solutions are:

• x = (-(-2) + √-4) / (2 * 1) = (2 + 2i) / 2 = 1 + i
• x = (-(-2) - √-4) / (2 * 1) = (2 - 2i) / 2 = 1 - i

So the correct answer to the student's question is A. x=1+i or x = 1- i.