common roots

Find common roots of equation z³+2z²+2z+1=0 and z¹⁹⁸⁵+z¹⁰⁰+1=0

4 Answers

z³+2z²+2z+1=0

z³ + 1 + 2z² + 2z

Hint: Now expand the first and second term

expand !!!!!!!!!!!!!!!!!!

Since first equation is cubic,
roots will be -1, e^{Â±i2Î /3}

substitute these roots in second equation and you'll see that the second equation satisfies at e^{Â±i2Î /3}, hence the common roots

here 1,w ,w^2 are satisfied.
the roots are 1,w,w^2.
now w^3=1.
substitute in second
we get 0.

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