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Find the value of $c$ so that the quadratic equation $4x^2 + 2x + c = 3x^2 - 8x$ has exactly one solution in $x$.

 Aug 21, 2023
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Find the value of $c$ so that the quadratic equation $4x^2 + 2x + c = 3x^2 - 8x$ has exactly one solution in $x$.   

 

Get everything on the left                                4x2 – 3x2 + 2x + 8x + c  =  0    

and combine like terms                                      x2          + 10x      + c  =  0      

 

The quadratic is now in the form ax2 + bx + c = 0         

For it to be a square, then b2 – 4ac must equal 0     

 

                                                                          102 – (4)(1)(c)  =  0       

 

                                                                           100  –  4c         =  0    

 

                                                                                              4c  =  100    

 

                                                                                                c  =  25      

.

 Aug 22, 2023

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