Let the rational roots (if any) be represented by p/q, where p, q ∈ℤ, p≠0, q≠0, and where p|-15 (constant term) and q|3 (leading coefficient).
Note: a|b means a divides b.
The possible candidates for rational roots are therefore:
±{1,3,5}/±{1,3}
or
±1, ±3, ±5, ±1/3, and ±5/3.
Evaluating f(x) for each of the candidates confirm that there are no rational roots.
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To find the real zeroes, we need to find the critical points (where f'(x) = 0) and evaluate f(x) at these points.
At all four critical points f'(x)<0, therefore there is only one real zero between 1.14 and infinity.
The single real (irrational) zero is at x=1.747 approx.
list all of the possible rational zeros of f(x) = 3x^5 - 7x^3 + 2x - 15.
1 answer