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Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

 Apr 26, 2024
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  2x^2 + 3x + 8x - x^2 + 4x + k has a double root    

 

  combine like terms                          (2x2 – x2) + (3x +8x + 4x) + k  

 

                                                           x2 + 11x + k    

 

  to have a double root,    

  i.e., both roots are the same,   

  the discriminate must equal zero        b2 – 4ac = 0    

 

                                                            (11)2 – (4)(1)(k)  =  0    

 

                                                             121 – 4k  =  0    

 

                                                                     –4k  =  –121    

 

                                                                          k  =  121 / 4    

.

 Apr 26, 2024

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