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.

Answer 1

Solution

Given the function

$f(x)=3x^3-2x^2+5x+2$

Since the coefficient of x^3 = 3

The coefficient of x^2 = - 2

The coefficient of x = 5

The coefficient of x^0 = 2

By applying the synthetic division with 3

The terms in the upper row = 3, -2, 5, 2

The terms in the middle row = 9, 21, and 78

And, the terms in the bottom row = 3, 7, 26, and 80

Since, 3> 0 and all the sign in the bottom row are positive.

Thus, 3 is the upper bond for real roots of this equation.