Final answer:
To find the least possible value of k for which the given equation has no real solution, we rearrange the equation to form a quadratic equation and solve for k using the discriminant formula. The least possible value of k is 50.
Step-by-step explanation:
To find the least possible value of k for which the given equation x(kx-56) = -16 has no real solution, we can start by rearranging the equation to form a quadratic equation:
x^2k-56x+16=0
We know that for a quadratic equation to have no real solutions, the discriminant (∆) must be negative. The discriminant is given by the formula ∆ = b^2 - 4ac.
In this case, a = k, b = -56, and c = 16. We now set ∆ to be less than 0 and solve for k:
(-56)^2 - 4(k)(16) < 0
3136 - 64k < 0
-64k < -3136
k > 49
Therefore, the least possible value of k for which the equation has no real solution is k = 50.