Question

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. k = -1; f(x) = 4x^3 - 2x^2 + 2x + 4; Lower bound? yes/no?

Answer 1

Answer:

Yes,  k is lower bound for the real zeros of the function.

Step-by-step explanation:

Lower Bound Theorem:

If you divide a polynomial function f(x) by (x - k), where k < 0, using synthetic division and this yields alternating signs, then k is a lower bound to the real roots of the equation f(x) = 0.

Given;

4x³ - 2x² + 2x + 4

k = -1

synthetic division;

-1 ]    4       -2        2        4

        ↓         -4        6       -8

---------------------------------------------

        4         -6       8          -4  

(the result has alternating signs, hence k is lower bound)

Thus, k is lower bound for the real zeros of the function.