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comment by akku (posted on 2 Feb 2008 18:09:00 IST)

heyyyyyyyyy frndsssssssssss be CAREFUL this rule of change of signs
gives the MAXIMUM NO OF +ve/-ve ROOTS

so u CANNOT SAY that there are 2 +ve roots fr 2 conseq changes
in sign in f(x) or 2 -ve roots fr 2 conseq changes in sign in f(-x) but u can say that there WILL be MAXIMUM 2 +ve and 2-ve roots
to illustrate the above statement:

eg: f(x)=x^2+x+1 0 changes in sign so 0+ve roots
f(-x)=x^2-x+1 2 changes in sign=>2 ive roots WHICH IS WRONG
u all must be knowing that f(x) has 2 complex roots w and w^2
ONE CAN ONLY CORRECTLY SAY THAT THELL BE NO +VE ROOTS
IN THE EXAMPLE U HAVE ASKED THE GOIITIANS TO ANS
max no of +ve roots=6
max no of -ve roots=2
no of complex roots=0(sry i cant exactly say whether it wod be max or minm becoz it may vary frm q to q)

SO THE METHOD STATED BY U WILL BE USEFUL TO KNOW IF THERE ARE NO +VE OR NO -VE SOLN IN OBJ QUESTIONS bt it may lead to ERRONEOUS results IF USED OTHERWISE TO KNOW NO OF REAL SOLUTIONS.

SO as a true frnd i wod just say - Himanshu and all the other goiitians pls be very cautious of such shortcuts given in books without their limitations LAY MORE STRESS ON CONCEPTS , such things are not evn mentioned in jee syllabus. NO SUCH QUESTION WILL BE ASKED IN HE EXAM which cannot be solvd using the basic concepts and confining to the constraints of the jee syllabus.

comment by i_love_physics (posted on 2 Feb 2008 22:27:22 IST)

the equation ax^2+b*modulous of x+c=0 will hav no real solution if n only if all of abc r positive..it wld hav solutions in othr wise ...for eg 3x^2+(modulous of x)-12 we split it as (3modx-3)(modx+4)=0
wen solving we get x=-1 n 1 ....the reason for ax^2 +modx*b+c has no real solutions wen all a b c are positive is tht...wen such a quadratic equation with all postive coefficents hav negative roots.. in our question d variable is mod x ....mod x cant b negative...tht y no solutions....nice article but i think u explained everything niclyyy...u shld hav added tht all a b c r positive.....oth wise ppl may think its a general rule....nice work anyway...

comment by i_love_physics (posted on 2 Feb 2008 22:29:32 IST)

and akku nice work yar... thnx a lott even i m noticing tht noww....thnkk u akku ...