IIT JEE , AIEEE Forum - Mathematics , Algebra

rudra.panda

if $\alpha^{13}=1$ and $\alpha\ne 1$

Find the quadratic equation whose roots are:

$\alpha+\alpha^3+\alpha^4+\alpha^{-4}+\alpha^{-3}+\alpha^{-1}$ and

$\alpha^2+\alpha^5+\alpha^6+\alpha^{-6}+\alpha^{-5}+\alpha^{-2}$

rudra.panda

Re:Quadratic Equation.

rudra.panda

Please help me go through the multiplication part.

Got a way for addition but please tell one for multiplication.

deedee

a^(13)=1

thus use

1+a^2+a^3.........+a^12=0

sum of roots is zero..............(rem we use it in complex nos ......complex cube root of unity ........ ??)

simplify d multiplication part and use d bove property

rudra.panda

expand? that will take ages. !