IIT JEE , AIEEE Forum - Mathematics , Algebra

man111

(1) if p(x)=x⁵+x³+1 has a root a₁,a₂,a₃,a₄,a₅

and q(x)=x²-2 than find out the value of q(a₁).q(a₂).q(a₃).q(a₄).q(a₅)

(2) if f(x)=x4+17x3+80x2+203x+125=0

than find a min polynomial g(x)

such that f(3+-3) = g(3+-3)

and f(5+-5) = f(5+-5).

raulrag009

edited

hsbhatt

Soln mein gadbad hey.

1 or -1 is not a root of the original eqn and the remainder when P(x) is divided by a₁ is P(a₁) = a₁⁵+a₁³+1.

Hey, the previous post just disappeared

saurabh_reincarnated

iss 2nd quest. ko koi karo yaar

dimaag kha raha hai mera

feynmann

1 . simple

let y = x^2 - 2 so

x^2 = y + 2

Now the given eqn becomes

x^ 3 ( x^2 + 1 ) = - 1

or , ( y + 2 ) ^ 3/2 ( y + 3 ) = - 1

or, ( y+ 2 ) ^3 ( y + 3 )^2 = 1

or , y^5 +............. + 71 = 0

product of its roots = - 71 ( ans )

saurabh_reincarnated

i need the 2nd ans . plz........

goiitians try the 2nd one................

feynmann

Check the last line of the 2nd qn .