PLEASE HELP
find a third degree polynomial equation in standard form with rational coefficents that has the roots -5 and 6+i

Question

PLEASE HELP 
find a third degree polynomial equation in standard form with rational coefficents that has the roots -5 and 6+i

anonymous · Answer

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anonymous · Answer

is what i have so far its just every time i multiply them together i get weird number so if someone could just multiply it out?

anonymous · Answer

Start by multiplying the two factors with the imaginary numbers. $$(x-(6-i))(x-(6-i))$$$$x ^{2} -6x+x i-6x-6i+36-x i+6i-i ^{2}$$The xi and 6i cancel out. i^2 = -1

So we have this $$x ^{2}-12x+37$$ Now multiply this by the other factor (x+5)

$$(x+5)(x ^{2}-12x+37)$$$$x ^{3}-12x ^{2}+37x+5x ^{2}-60x+185$$$$x ^{3}-7x ^{2}-23x+185$$