Answer:
At either b = -12 or b = +14, the equation has a unique solution.
Step-by-step explanation:
The quadratic equation w^2 + bw + 36 = 0 has three coefficients: a = 1, b and c = 36. This equation will have a unique solution (which is also real, not complex) if the discriminant b^2 - 4ac is zero. Here b^2 - 4ac can be rewritten as
b^2 - 4(1)(36). Setting this equal to zero, we get
b^2 - 144 = 0, which is equivalent to b^2 = 144. Thus, b = ± 12.
At either b = -12 or b = +14, the equation has a unique solution.
