Find the largest integer value if the roots are imaginary and the smallest integer value if the roots are real and unequal in the equation \(4x^2-12x+k=0\)
+128407 If the roots are imaginary, the discriminant is < 0
So.....
(-12)^2 - (4)(4)k < 0
144 - 16k = 0
144 < 16k
9 < k
Since any k > 9 produces non-real solutions, there is no largest integer value that applies
If the roots are real, but unequal, then
(-12^2) - (4)(4)k > 0
144 > 16k
9 > k
Likewise....since any k < 9 produces two unequal real roots, there is no smallest integer value that applies, either
