SOLUTION: Consider g(x) = 2x^3 - x^2 + 2x -1
(a) Tell the maximum number of real zeros that the function may have. Do not
attempt to find the zeros.
(b) List the potential rational
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Question 1189362: Consider g(x) = 2x^3 - x^2 + 2x -1
(a) Tell the maximum number of real zeros that the function may have. Do not
attempt to find the zeros.
(b) List the potential rational zeros. Do not attempt to find the zeros.
(c) Determine the real zeros of g and write g in factored form.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
(a) A polynomial of degree n has a maximum of n real zeros. This polynomial is degree 3, so the maximum number of real zeros is 3.
(b) (+/-) (p/q), where p is a factor of the constant term (-1) and q is a factor of the leading coefficient (2). So the possible rational zeros are
1, -1, 1/2, and -1/2.
(c)
The coefficients 2, -1, 2, -1 show us this can easily be factored by grouping:
The factor (x^2+1) produces a pair of complex roots. The only real root is 1/2, coming from the factor (2x-1).
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