Question

X(kx-56)=-16

In the given equation, k is an integer constant. If the equation has no real solution, what is the least possible value of k?

Answer 1

The least possible value of k in the equation x(kx-56) = -16 that would result in no real solutions is 50.

Step-by-step explanation:

To find the least possible value of k that would result in no real solutions, let's first simplify the equation:

x(kx-56) = -16

Expanding the equation, we get:

kx^2 - 56x + 16 = 0

The equation will have no real solutions if the discriminant, b^2 - 4ac, is less than zero. In this case, the discriminant is:

(-56)^2 - 4(k)(16) = 3136 - 64k

To have no real solutions, 3136 - 64k < 0. Solving this inequality for k:

64k > 3136

k > 49

The least possible value of k that would result in no real solutions is 50.