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

 Nov 15, 2023
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Find the constant $k$ such that the quadratic $2x^2 + 3x + 8k + 3x^2 + 2x + k$ has a double root.  

 

                                                2x2 + 3x + 8k + 3x2 + 2x + k    

 

                                                combine like terms, and arrange in standard form ax2 + bx + c  

 

                                                 5x2 + 5x + 9k  

 

                                                 an equation has a double root when its discriminant equals zero   

 

                                                 b2 – 4ac =  0  

 

                                                 52 – (4)(5) • 9k  =  0  

 

                                                         25 – 180k  =  0  

 

                                                              – 180k  =  – 25  

 

                                                                       k  =  25 / 180  

 

                                                                       k  =  5 / 36  

.

 Nov 17, 2023

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