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Find approximations to within 10−5 to all the zeros of each of the following polynomials by first finding the real zeros using Newton s method and then reducing to polynomials of lower degree to determine any complex zeros.
a. f (x) = x4 + 5x3 − 9x2 − 85x − 136
b. f (x) = x4 − 2x3 − 12x2 + 16x − 40
c. f (x) = x4 + x3 + 3x2 + 2x + 2
d. f (x) = x5 + 11x4 − 21x3 − 10x2 − 21x − 5
e. f (x) = 16x4 + 88x3 + 159x2 + 76x − 240
f. f (x) = x4 − 4x2 − 3x + 5
g. f (x) = x4 − 2x3 − 4x2 + 4x + 4
h. f (x) = x3 − 7x2 + 14x - 6 |
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