Question

find all other zeros of P (x)= x^3-2x-4, given that -1-i is a zero. ( if there is more than one zero, separate them with commas.)

Answer 1

Since this is a cubic equation, there are 3 possible zeroes

x= 2, x = -(1-i) and x = -(1+i)

We can solve the equation by factoring the P(x)

`(x-2)(x^2+2x+2)`

We can get the complex factor of the second term

`(x-2)(x+(1+i))(x+(1-i))_{}`

Given this factor, the function P(x) will be zero if

`x\text{ = 2, -1-i, and -1+i}`