Question

The equation w^2+bw+36=0 has a unique solution if b=___ or b=____

Answer 1

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.