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The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

 Apr 24, 2024
 #1
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                                                 x^2-mx+24 = 10   

 

subtract 10 from both sides      x2 – mx + 14  =  0   

 

integers that multiply to 14        (+7)(+2)   

                                                  (–7)(–2)   

                                                  (+1)(+14)   

                                                  (–1)(–14)  

 

possible values of m                   –9   

                                                   +9   

                                                  –15   

                                                  +15   

 

total number of

possible values of m                      4    

.

 Apr 25, 2024

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