IIT JEE , AIEEE Forum - Mathematics , Algebra

AAKRITI

Find the values of parameter r so that the biquadratic x^{4_{- 4x}3 _{- 8x}2}_{^{+ r = 0 has (i) no real roots (ii) all roots real and distinct (iii) exactly 2 real roots}}

Asmita

x^4--4x³-8x²+r=0

(i) suppose the roots to be (a+ib),(a-ib),(c+id)&(c-id)because complex roots occur in pair if the coefficients are rational.

Now use the relations between roots & coefficients & compare the relations I hope you will get the answer.

In the same way attempt the remaining parts of the ques.

I have not solved the ques. yet. As soon as I solve it I'll give you the detailed sol.

AAKRITI

Asmita I tried this method but no result is coming. Experts pl suggest some other way.

Asmita

Aakriti are u sure because i am hoping u will arrive at some ans.

try this if r=a^2+b^2+c^2 where a,b,c are real

then r>=0 this thing has relevance in this ques.

have u tried this?

rahul_c

if f(x) has n equal roots then f '(x) will have n-1 equal roots

you can use this condition

say,
if f(x) has no root then f ' (x) will also have no root

AAKRITI

Rahul please give your full solution.

hit_ur_heart

rahul_c i told u several times taht u r giving wrong answers y dunt u understand this, please do not give wrong answer untill and unless u understand the concept carefully , ur concepts are wrong , please see this example

f(x) = (x-3)^2 + 4
this function has no solution but , f``(x) = 2(x-3) has real solution , i am telling u again , u only know answers , why & how terms are immaterial to u, figure it out , otherwise u know very will what will happen

hit_ur_heart

and whosoever ask this question , please understand that this is not in the JEE syllabus ( biquadratic equation) , and if it will come then it will be some special case.

If u wanna know solution of this question i can write that here , but nothin will be happened by that , it willl be very good for u if u give ur time to topics which are in syllabus

Thnxs

AAKRITI

Listen , this is very much in the syllabus.. I am never free to do those things which are not in the course neither am I interested to do such things at this point of time . It came in my institute's test series . The discussion of the test will be on 17th and I am having my physics pre board on that day, so I thought of asking this to the experts. If you can provide any solution , I would be thankful.

AAKRITI

Do tell me if this can be solved using graphs.I've tried all other ways.

hit_ur_heart

well akriti , what i can say i also cleared JEE few years ago, i never requires this , even at that time paper was more tougher than now ............................neways this can be solved by converting it to standard form of biquadratic equation.

rahul_c

hit_ur_hit whatever i have written is directly picked up from

HALL AND KNIGHT ALGEBRA
CHAPTER - THEORY OF EQUATIONS .CONTEXT NUMBER 557

AAKRITI

Hi Asmita, thanks for giving me so many salutes .. This is not to offend you or anything as such.. but I don't think I actually deserve all of them.. I mean you have even given me salutes on my own replies.

vikrant_sharma

i think what Rahul has said is correct . i looked into hall and knight it's there

perhaps this sum can be solved by maxima minima condition and thereby drawing the graph .Although i myself haven't been able to do so.

(No offence)mr hit_ur_heart should be polite to peple and respect others.if he has the solution he must post , without beating around the bush

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