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Given that three -3 I zero, find the remaining zero of the following polynomial function use the CONGUGATE root theorem if applicable write the exact answer do not round separate multiple answers with a comma

Given that three 3 I zero find the remaining zero of the following polynomial function use the CONGUGATE root theorem if applicable write the exact answer do no class=

Respuesta :

Given:

[tex]f(x)=x^4+6x^3+22x^2+24x+576[/tex]

and the one solution is 3-3i.

Find: remaining zeroes

Explanation:

[tex]f(x)=[x-(3-3i)][x-(3+3i)]Q(x)[/tex]

where Q(x) is second order polynomial.

then

[tex]Q(x)=x^2+12x+32[/tex][tex]x^2+12x+32=(x+4)(x+8)[/tex]

so the solution of the equation is 3+3i,3-3i, -4 and -8