Question

The complex solution's of which equation have a real component of 4?

A) x² + 8x + 16 = -21
B) x² - 4x + 4 = -25
C) x² + 4x + 4 = -25
D) x² - 8x + 16 = -21

Answer 1

The complex solutions of the equation x² + 4x + 4 = -25 have a real component of 4.

Step-by-step explanation:

The complex solutions of the equation x² + 4x + 4 = -25 have a real component of 4. To find the complex solutions, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 4, and c = -29. Substituting these values into the formula, we have:

x = (-4 ± √(4² - 4(1)(-29))) / (2(1))

x = (-4 ± √(16 + 116)) / 2

x = (-4 ± √132) / 2

The solutions, therefore, are x = (-4 + √132) / 2 and x = (-4 - √132) / 2.