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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 \(4x^2-12x+k=0\)

Guest Nov 18, 2017

#1**+1 **

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

CPhill Nov 18, 2017