Find the largest integer k such that the equation
5x^2 - kx + 8 = 4x^2
has no real solutions.
+128460 5x^2 -kx + 8 = 4x^2 .....subtract 4x^2 from both sides
x^2 - kx + 8 = 0
We will have no solutios when the discriminant .... (-k)^2 - 4 (1) (8) < 0
So....simplifying and rearranging we have
k^2 < 32
The integer values that make this true are [ -5 ...... 5 ]
So.....5 is the largest integer that produces no real solutions
