Question

for the given function, determine consecutive values of x between which each real zero is located. f(x)=-14x^4-7x^3-18x^2+17x+11

Answer 1

(-1, 0) and (0, 1)

Explanation:

There is one sign change, so one positive real root. f(0) = 11 and f(1) = -11, so the positive real root is in the interval (0, 1).

When odd term signs are negated, the signs become (- + - - +), so there are 3 sign changes. This means there is 1 or 3 negative real roots. f(-1) = -31, so there is a negative real root in the interval (-1, 0).

When we do synthetic division by x+1, we get alternating signs on the bottom line, indicating -1 is a lower bound on real roots.

Real roots are located between -1 and 0, and between 0 and +1.

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The graph of the function confirms this answer.