16x^4+8x^3+17x^2+8x+1

I have tried it but i keep getting the wrong roots can someone solve this?

is that all equal to zero.

Like so,
16x^4+8x^3+17x^2+8x+1=0

it dosent say on the worksheet, it says


g(x)=16x^4+8x^3+17x^2+8x+1

That is the same thing.

What are you trying to do? Simplify the equation.

oh well we have to figure out the roots but this one im lost on how to finish it

(4 x+1)^2 (x^2+1) is the simplified version

and x=-1/4
and x=+i and x=-i

To solve the given polynomial equation, we can make use of the Rational Root Theorem and synthetic division. Here's how you can approach it step by step:

1. Begin by applying the Rational Root Theorem. It states that if a polynomial equation has a rational root, it must be in the form of p/q, where p is a factor of the constant term (in this case, 1) and q is a factor of the leading coefficient (in this case, 16).

2. List all possible factors of 1: ±1.
List all possible factors of 16: ±1, ±2, ±4, ±8, ±16.

3. Substitute each potential rational root into the equation and check if any of them satisfy it. You can do this by synthetic division or by using a graphing calculator.

Let's use synthetic division to test each potential root:

For the root x = 1:
1 | 16 8 17 8 1
-16 -8 9 17
--------------------
0 -8 9 17
The remainder is not zero, so x = 1 is not a root.

For the root x = -1:
-1 | 16 8 17 8 1
-16 8 -25 17
--------------------
0 8 -8 25
The remainder is not zero, so x = -1 is not a root.

No rational roots were found from the list of possible factors. This means either the roots are irrational or complex. To find the remaining roots, we need to use numerical or graphical methods.

To proceed, you can either utilize numerical methods such as Newton's method, or you can use a graphing calculator or software to determine the approximate roots.