Determine all the zeros of the polynomial P(x)=x3+7x2+18x+18.
The possible rational zeros are the factors of 18 which are ±1,±2,±3,±6,±9 and ±18. By using synthetic division and by trial and error,
Thus,
P(x)=x3+7x2+18x+18=(x+3)(x2+4x+6)
To find the complex roots, we use quadratic formula.
x=−4±√42−4(1)(6)2(1)=−4±√−82=−2±√2i
Thus, the zeros of P are −3,−2±√2i and −2−√2i
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