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For what values of \(j\) does the equation \((2x+7)(x-5) = -43 + jx\) have exactly one real solution? If you find more than one, then list the values separated by commas.\(\)

 Mar 20, 2024
 #1
avatar+128794 
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2x^2 - 3x - 35 =  -43 + jx

 

2x^2  - ( 3 + j)x + 8   =  0

 

To only have one solution,  the discriminant = 0

 

(3 + j)^2  - 4 * 2 * 8  =   0

 

(3 + j*2  -  64  = 0

 

(3 + j)^2  =   64               take both roots

 

3 + j  =  8                     3 + j =  -8

 

j =  5                              j =  -11

 

cool cool cool

 Mar 20, 2024

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