Tuesday, December 15, 2015

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 48

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±424(1)(6)2(1)=4±82=2±2i

Thus, the zeros of P are 3,2±2i and 22i

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