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For what real values of k does the quadratic 12x^2 + kx + 27 = 8x^2 + 18 + 14x^2 + 32 have nonreal roots?  Enter your answer as an interval.

 May 10, 2024
 #1
avatar+128796 
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12x^2 + kx + 27 = 8x^2 + 18 + 14x^2 + 32

 

Rearrange as

 

10x^2  - kx  + 13  =  0

 

This will have non-real roots when the discriminant < 0

 

k^2  - 4(10)(13)  <  0

 

k^2  <   520

 

k < sqrt (520)      or   k > -sqrt (520)

 

( -sqrt 520 , sqrt 520) 

 

cool cool cool

 May 10, 2024

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