Answer:
<u>The correct answer is D. -5 +/- i√2</u>
Step-by-step explanation:
Let's solve for x, the equation given to us, this way, using the quadratic formula:
x = (- b +/- √b² - 4ac)/2a
Replacing with the real values, we have:
x = (-10 +/- √10² - 4 * 1 * 27)/2
x = (-10 +/- √100 -108)/2
x = (-10 +/- √-8)/2
x = (-10 +/- √-1 * 4 * 2)/2 Let's recall that √-1 = i
x = (-10 +/- 2i√2)/2
x = 2 (-5 +/- i√2)/2 (Dividing by 2 both the numerator and the denominator)
<u>x₁ = -5 + i√2</u>
<u>x₂ = -5 - i√2</u>
<u>The correct answer is D. -5 +/- i√2</u>