prove that....

If a,b,c are odd integers, prove that ax2 + bx + c = 0 does not have a rational

number solution.

Please show the procedure......

1 Answers

11
SANDIPAN CHAKRABORTY ·

check

http://www.targetiit.com/iit-jee-forum/posts/quad-14741.html

2) let the roos be p/q and r/s

then the quadratic become s

(x-p/q)(x-r/s)=0

comparing this with ax2+bx+c we get

qs=a -(ps+rq)=b and pr=c

this means q,s should be odd because their product is an odd integer a.

even p,r should be odd in a similar way

this mean s ps+rq will be evn .. but this is equal to -b whihc is an even integer..

hence a contradictoon..

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