Given one zero of the polynomial function, find the other zeros. f(x)=2x^3+3x^2-3x-2; -2
1 answer:
Answer:
{-1/2, 1}
Step-by-step explanation:
You can divide the given polynomial by the factor (x +2) to find the remaining quadratic. That can be factored in the usual way to find the remaining zeros, or other means can be used. Such "other means" include graphing and the use of the quadratic formula.
The first attachment shows the synthetic division of f(x) by (x+2). The quotient is 2x^2 -x -1, which factors as ...
2x^2 -x -1 = (2x +1)(x -1)
The zeros are the values of x that make these factors zero: -1/2, +1.
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My favorite way to find the roots of any higher degree polynomial is to use a graphing calculator. The second attachment shows that method.
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