Final answer:
The equation 2r² + 5r + 8 = 0 is solved using the quadratic formula. The solutions are expressed in a + bi form where a = -5/4 and b is ±√39/4.
Step-by-step explanation:
To solve the equation 2r² + 5r + 8 = 0, we can use the quadratic formula, which is -b ± √b² - 4ac over 2a. First, identify a, b, and c in the equation where a=2, b=5, and c=8. Substitute these values into the quadratic formula.
Applying the quadratic formula, we get:
- r = (-5 ± √(5² - 4 * 2 * 8)) / (2 * 2)
- r = (-5 ± √(25 - 64)) / 4
- r = (-5 ± √(-39)) / 4
- r = (-5 ± √i*√39) / 4
Where √i is the imaginary unit. Since √-39 is imaginary, we express it as √i*√39. Thus, the solution is in a + bi form, where a = -5/4 and b = ±√39/4.