Answer :
Final answer:
The upper and lower bounds on the zeros of the function f(x) = 10x^4 + x^3 - 50x^2 - 7x + 19 are -2 and 3, respectively.
Explanation:
To determine the upper and lower bounds on the zeros of the function f(x) = 10x^4 + x^3 - 50x^2 - 7x + 19, we can use the concept of the Intermediate Value Theorem. The Intermediate Value Theorem states that if a function is continuous on an interval [a, b] and takes on values f(a) and f(b) with opposite signs, then the function must have at least one zero in the interval (a, b).
By using synthetic division or graphing techniques, we can find the intervals where the function changes sign. In this case, we can see that the function changes sign between x = -2 and x = -1, between x = 0 and x = 1, between x = 1 and x = 2, and between x = 2 and x = 3. Therefore, we can conclude that the zeros of the function f(x) = 10x^4 + x^3 - 50x^2 - 7x + 19 lie between these intervals.
So, the upper and lower bounds on the zeros of the function f(x) = 10x^4 + x^3 - 50x^2 - 7x + 19 are -2 and 3, respectively.
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