IIT JEE , AIEEE Forum - Mathematics , Algebra

neeraj_agarwal_1990

Let ab,c,d be the roots of x⁴+x²+1=0.Then the equation whose roots are a²,b²,c²,d² is ?

[ans: (x+x+1)²]

please explain..

saarika

the ans should be (x²+x+1)². the eqn having sq of the roots of a given eqnf(x),is f(

x). so(^{[ ]}

x)⁴+(^{[ ]}

x)²+1 =x²+x+1.since the eqn should be of fourth degree, it should be squared.hence ans is (x²+x+1)².

DON007

hey man.................dont be in tension , bcoz main hoon naa....

kidding...........

now look in these questioons...............................

put y= x²

u will get y²+y+1=0

then y= w

y= w²

^{now as}y = x²

x= w, -w , w², -w²..................

now as we squre them (as in ur problm)............

we get

x= w², w², w^4,w⁴

x= w², w², w, w

2 similar roots.........therefore.............

equation is............[ (x-w) (x-w²)]²

⁼[ x²+ x +1]²(ans)

understood...........

thanku

amar.gupta

Dear,

I think you have got the ans . feel free to ask if doubt any