Find the largest integer such that the equation

5x^2 - mx + 8 = 4x^2 - 12

has no real solutions.

Guest Jul 2, 2022

#1**0 **

Simplify to get:

\(x^2-mx+20=0\)

Now, for this Quadratic to have no real solutions, it should not intersect the x-axis.

So, the discriminant , which is: \(b^2-4ac\) must be less than zero.

So:

\(b^2-4ac<0\)

\(\iff m^2-80 <0\) (Now we have to solve this Quadratic inequality for m).

The critical values: \(m=\pm 4\sqrt{5}\)

Next, sketch (*) and place the critical points, you want the region below the x-axis (Hence, between the critical values):

Thus, \(-4\sqrt{5}

Since hte question is asking about the largest integer m, let us convert this to decimal:

\(-8.94427..

Therefore, the largest integer m, is: \(m=8\) is the desired solution.

Hope this helps!

Guest Jul 3, 2022