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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?

 Jul 14, 2024
 #1
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x2 – mx + 24 = 10   

x2 – mx + 14 = 0   

 

the coefficient of x is the sum of the factors of 14   

the integer factors of +14 are (+2, +7) and (–2, –7)   

                                         and (+1, +14) and (–1, –14)   

 

So m could equal +9 or –9 or +15 or –15   

 

Therefore, m could have 4 possible values    

.

 Jul 14, 2024

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