Question 1117693: With the polynomial: f(x) = 5x^3 + 8x^2 -4x + 3
a. The Fundamental Theorem of Algebra states that this polynomial has ______ roots.
b. Find f(-x).
c. Use Descartes’ rule:
Number of positive real zeros
Number of negative real zeros
Number of imaginary real zeros
d. Use the Rational Root Theorem to determine the possible rational roots of f(x).
correct?: ±1, ±(1/5), ±3, ± (3/5)
e. Of the possible rational roots above, which ones are roots?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! With the polynomial: f(x) = 5x^3 + 8x^2 -4x + 3
a. The Fundamental Theorem of Algebra states that this polynomial has 3 roots.
b. Find f(-x) = -5x^3 + 8x^2 + 4x + 3
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c. Use Descartes’ rule
Number of positive real zeros:: <= # of sign changes in f(x) = 2 (actually 0)
Number of negative real zeros:: <= # of sign changes in f(-x) = 1 (actually 1)
Number of imaginary real zeros:: (actually 2)
d. Use the Rational Root Theorem to determine the possible rational roots of f(x).
correct?: ±1, ±(1/5), ±3, ± (3/5)
e. Of the possible rational roots above, which ones are roots? (actually none)
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Cheers,
Stan H.
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