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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 \(4x^2-12x+k=0\) 

 Nov 18, 2017
 #1
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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

 

 

 

cool cool cool

 Nov 18, 2017

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