Find a polynomial f(x) Of degree 4 and -4 -2 and i are zeros of 3 multiplicity 2
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1 Answer

Duplicated zero must be -4, because the other two zeroes are complex: -2+i and -2-i.

Polynomial appears to be (x+4)²(x+2-i)(x+2+i)=

(x²+8x+16)(x²+4x+5)=

x⁴+4x³+   5x²

   +8x³+32x²+40x

            16x²+64x+80=

x⁴+12x³+53x²+104x+80. There are 3 zeroes.

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