Answer:
n = (1/2)(-1 ± i√2)
Explanation:
Among the several ways in which quadratic equations can be solved is the quadratic formula. Putting to use the coefficients {12, 12, 9}, we obtain the discriminant, b^2 - 4ac: 12^2 - 4(12)(9) = 144 - 432 = -288. The negative sign of this discriminant tells us that the quadratic has two unequal, complex roots. These roots are:
-b ± √(discriminant)
n = ---------------------------------
2a
Here we have:
-12 ± √(-288) -12 ± i√2√144 -12 ± i12√2
n = ---------------------- = ------------------------ = --------------------
2(12) 24 24
or:
n = (1/2)(-1 ± i√2)