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For what values of j does the equation (2x + 7)(x - 15) = -43 + jx have exactly one real solution? Express your answer as a list of numbers, separated by commas.

 Jan 12, 2021
 #1
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(2x + 7)  ( x - 15)  =   -43 + jx

 

2x^2 -  23x  -  105   =  -43  +  jx

 

2x^2   - (23+ j)x  - 62  =   0

 

If this  has one real root, then the discriminant  =   0  .......so......

 

(23 + j)^2   - 4 (2) (-62)   = 0

 

(23 + j)^2  +  496  =  0

 

(23 + j)^2  =   -496        take both roots

 

23 + j =  4sqrt (31) i                23   +  j  =   -4 sqrt (31)  i 

 

j =  4sqrt (31) i  - 23                    j =     -4sqrt (31)  - 23

 

 

cool cool cool

 Jan 12, 2021

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