1.

Cosider f(x)ax^(3)+bx^(2)+cx+d, where a,b,c,dinRanda!=0. If the equation f(x)=0 has three real roots alpha,beta,gamma such that alphaltbetaltgamma andL=Lim(|ax^(3)+bx^(2)+cx+d|)/(ax^(3)+bx^(2)+cx+d), where m in R, then which of the following may be correct ?

Answer»

`L=1ifbetaltmltgamma`
`L=-1ifalphaltmltbeta`
`L=-1ifbetaltmltgamma`
L=does not exist, if `m=beta`

SOLUTION :
`{:("when "betaltmltgamma_(,),"when "alphaltmltbeta,or""betaltmltgamma,),( :.F(x)gt0,f(x)lt0,:.f(x)lt0,),( :.L=1, :.L=-1,:.L=-1,):}`
When m `=beta,"the" underset(xtobeta)LIM(|ax^(3)+BX^(2)+cx+d|)/(ax^(3)+bx^(2)+cx+d)=` does not exist
As L.H.L. and R.H.L. will differ by NEGATIVE sign.


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