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If a,b and c are odd integers prove that the quadratic ax2+bx+c = 0 has no rational roots.
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to have rational roots we D shud be a perfect square so b^2-4ac=q^2 (let) if a,b,c are odd integers so q will also be odd........u can check it... so assume a,b,c,q to be of the form 2t+1,2u+1,2v+1,2w+1 (b+q)(b-q)=4ac putting them u get; (u+w+1)(u-w)=(2t+1)(2v+1) now observe that left hand side is always even...u can check by putting any arbitary values and right hand side is always odd.... so our assumption that b^2-4ac=q^2 is wrong so there is no value of q that can satisify this eqn.......... hence this eqn does'nt have rational roots............. nudge if u hav doubt rate if u like !! |
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Who says nothing is impossible. I've been doing nothing for years !!.............. I know KUNG FU KARATE and 47 other dangerous words............. |
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