Solve each equation in Exercises 83–108 by the method of your choice.x^2 - 6x + 13 = 0

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. x^2 - 8x + 16 = 0

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. 9x^2 + 11x + 4 = 0

Solve each equation in Exercises 83–108 by the method of your choice.x^2 - 2x = 1

Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) i, -i

Solve each equation in Exercises 83–108 by the method of your choice.3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)

In Exercises 115–122, find all values of x satisfying the given conditions.y1 = 2x/(x + 2), y2 = 3/(x + 4), and y1 + y2 = 1

In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression.3/(2x^2 + 4x - 9)

In Exercises 127–130, solve each equation by the method of your choice.√2 x^2 + 3x - 2√2 = 0