Condition for two consecutive integral solution
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I need to find the values of k(possible) for which the quadratic equation
x2+2kx+k=0x2+2kx+k=0
will have integral roots. So I assumed roots to be a,ba,b Then I got the condition a+b=−2ka+b=−2kand a⋅b=ka⋅b=k; so combining these I get a+b+2ab=0a+b+2ab=0; And now I need to find the integral values of a,ba,b for which this equation is satisfied,how should I procced from here?? Also is there any shorter much elegant way to do this question. (Note-A hint would suffice)
x2+2kx+k=0x2+2kx+k=0
will have integral roots. So I assumed roots to be a,ba,b Then I got the condition a+b=−2ka+b=−2kand a⋅b=ka⋅b=k; so combining these I get a+b+2ab=0a+b+2ab=0; And now I need to find the integral values of a,ba,b for which this equation is satisfied,how should I procced from here?? Also is there any shorter much elegant way to do this question. (Note-A hint would suffice)
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