Find the complex zeros of each polynomial and right the polynomial and right the polynomial in factored form

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#1

Find the complex zeros of each polynomial and right the polynomial and right the polynomial in factored form. a) f(x)=x^3+13 ^2+57x+85. b) g(x)=x^4+5x^2+4. c) f(x)=x^4+3x^3-19x^2+27x-252

Answer:

a) f(x)=(x+5)(x^2+8x+17)=0; apply quadratic formula to quadratic equation and you get complex zeros = -4+i, -4-i.

b) g(x)=(x^2+4)(x^2+1)=0; solve for each factor and you get complex zeros = -2i,2i,-i,i

c) f(x)=(x-4)(x+7)(x^2+9)=0; both first factors give real roots, only last factor gives complex roots. Solve for it and get that complex zeros = -3i, 3i