Question

If `alpha, beta , gamma, delta` are the roots of the equation `x^4+x^2+1=0` then the equation whose roots are `alpha^2, beta^2, gamma^2, delta^2` is

Answer 1

let `x^2=t`
`t^2+t+1`
`1+w+w^2=0`
`x=e^(ipi/3),-e^(ipi/3),e^(i2.3pi)...`
`alpha^2beta^2gamma^2rho^2=e^(12/3pi)...`
`w^6=1`
`alpha^2+beta^2+gamma^2+rho^2=e^(i2/3pi),e^(i2/3pi)+e^(i4/3pi+e^(i4/3pi)`
`=2(w+w^2)=-2`
option b is correct.