Which of the following is a solution of x² - 10x = -36?
10 + 2i√11, 5 + i√11, 5 - i√11, 10 - 2i√11

Solution:

The given equation is

x² - 10x + 36 = 0

The above equation is a quadratic equation of the form ax² + bx + c

The roots of the equation a² + bx + c are:

(-b ± √b² - 4ac)/2a

Here a = 1, b = -10, c = 36

b² - 4ac = 10² - 4(1)(36) = 100 - 144 = -44

Therefore

√b² - 4ac = √-44 = √-4 × 11 = 2√11 × -1 = 2√11 × √-1 = 2i√11 (√-1 = i)

The roots of the given equation are 5 + i√11 and 5 - i√11 which are complex conjugates.

Which of the following is a solution of x² - 10x = -36?

Summary:

The roots of the given equation are 5 + i√11 and 5 - i√11 which are complex conjugates.