IIT JEE , AIEEE Forum - Mathematics , Algebra

Mr.IITIAN007

If

are the roots of the equation

ax⁴+bx³+cx²+dx+e then what is the value of

(1+

²)(1+

²) (1+

²)(1+

²)?????????????????

amitsingh

Question is not clearly visible

jaysunantony

LET ME TAKE THE ROOTS AS m,n,o,p .................

ax4+bx3+cx2+dx+e = a(x-m ) ( x-n ) (x-o) ( x-p)

put x= i [iota]

u will get, a [m-i] [n-i] [o-i] [p-i] = a-bi-c+di+e

[.........infact u get[i-m] but multiply each with -1.]

put x= -i

u will get a [m+i] [n+i] [o+i] [p+i] = a+bi-c-di+e

now multiply both eqns.

u will get, answer.................... rate me...........and soory, it didnt knock my head off my neck

tarun007

jay's solution was good one.

here is another good soln.
let m,n,o,p be the roots of the given equation
first substitute x by (x-1)^1/2 in the given equation
this will change the roots of the equation from m,n,o,p to m^2+1 etc.
now separate the under roots on one side and the rest on the other
square the whole equation and get the reqd biquadratic eqn.
the (coefficient of x^0)/(coeff of x^4) is the required answer.

rate me if i am correct.

jaysunantony

HI tarun007,

THANKS............

and my name is Jaysun Antony.

jaysunantony

HI tarun007,

pLEASE EXPLAIN THE SOLUTION ..................YOU HAVE GIVEN.........

first substitute x by (x-1)^1/2 in the given equation
this will change the roots of the equation from m,n,o,p to m^2+1 etc.

HOW ?.................

PLS POST THE COMPLETE SOL..............I HAD RATED YOU................

AND WILL AGAIN............

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