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Suppose the roots of the polynomial x^2-mx+n are positive prime integers (not necessarily distinct). Given that m<20 how many possible values of n are there?

 Aug 6, 2020
 #2
avatar+110713 
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Suppose the roots of the polynomial x^2-mx+n are positive prime integers (not necessarily distinct). Given that m<20 how many possible values of n are there?

 

Let the roots be a and b where are and b are positive prime integers.

then

we have   (x-a)(x-b) = x^2-(a+b)x +ab

 

m= a+b     

n= ab 

which means that m and also n are positive. 

 

 

So I count 17 possible values of n

 Aug 21, 2020
 #3
avatar+259 
+1

Thanks for the clear explanation Melody! :-D 

 

But your answer is incorrect.

 Aug 21, 2020
edited by HelpBot  Aug 21, 2020

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