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 = 2; f(x) = 2x3 + 4x2 + 2x - 4; Lower bound?

Answer 1

Answer: k = 2 is the upper bond of the given equation.

Step-by-step explanation:

Here, Given function,  

$f(x) = 2x^3 + 4x^2 + 2x - 4$;

Since, the coefficient of $x^3$ = 2

The coefficient of $x^2$ = 4

The coefficient of $x$ = 2

And, the constant term = - 4

By applying the synthetic division with 2,

The terms in the upper row = 2, 4, 2 and - 4

The terms in the middle row = 4, 16 and 36

And, the terms in the bottom row = 2, 8, 18 and 32

Since, 2> 0 and all the sign in the bottom row are positive.

Thus, 2 is the upper bond for real roots of this equation.

Answer 2

Answer:

upper bound

Step-by-step explanation:

k=2 is not lower bound as seen above