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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.)

find all other zeros of P (x)= x^3-2x-4, given that -1-i is a zero. ( if there is-example-1
User Frohlich
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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}

User HammerSpb
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