SOLUTION: Given a>b>c>0, the function f(x)= x(x-a)(x+b)(x-c) is less than or equal to zero on the intervals a. (-∞, -b), [0,a] and [c,∞) b (-∞,-b], [0,c] and [a,∞) c. [-b,0] an

Question 1181603: Given a>b>c>0, the function f(x)= x(x-a)(x+b)(x-c) is less than or equal to zero on the intervals
a. (-∞, -b), [0,a] and [c,∞)
b (-∞,-b], [0,c] and [a,∞)
c. [-b,0] and [c,a]
d.[-a,-c] and [0,b]
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The polynomial is degree 4 with positive leading coefficient, so the value goes to infinity for both large negative and large positive values.

The zeros of the function are all single; from left to right they are -b, 0, c, and a. So the function value is

(1) greater than 0 on (-infinity,-b)
(2) less than or equal to 0 on [-b,0]
(3) greater than 0 on (0,c)
(4) less than or equal to 0 on [c,a]
(5) greater than 0 on (a,infinity)

ANSWER: c. [-b,0] and [c,a]

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