Need help with finding roots and zeros of polynomial functions

twinkasoo

New member
Joined
Dec 8, 2015
Messages
1
Hi if someone could help me with the following questions that would be great! (with work)

1. Find the roots of the following equations

a) 0=x^4 - 8x^2 + 16

b) 2x= 4x^3 - 2x^2

2. Find all of the zeroes in the following

P(x)= x^4 - 4x^3 - 16x^2 + 21x + 18

3.
Is (x+2) a factor of x^3 - 3x^2 - 4x





Thanks so much!!!! :p:D
 
Hi if someone could help me with the following questions that would be great! (with work)

1. Find the roots of the following equations

a) 0=x^4 - 8x^2 + 16

b) 2x= 4x^3 - 2x^2

2. Find all of the zeroes in the following

P(x)= x^4 - 4x^3 - 16x^2 + 21x + 18

3.
Is (x+2) a factor of x^3 - 3x^2 - 4x

Thanks so much!!!! :p:D

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "
Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
 
Hi if someone could help me with the following questions that would be great! (with work)
Sorry but, as you saw in the "Read Before Posting" thread that you read before posting (right?), we don't "do" students' work for them, nor do we give out answers, especially not when the poster has shown no efforts of his/her own. :oops:

1. Find the roots of the following equations

a) 0=x^4 - 8x^2 + 16

"Finding the roots" means "finding the zeroes" or, which means the same thing, setting the thing equal to zero and solving the equation. So what have you tried so far?

This particular polynomial is quadratic in form:

. . . . .\(\displaystyle (x^2)^2\, -\, 8(x^2)\, +\, 16\, =\, 0\)

Did you try factoring? (here) Or did you apply the Quadratic Formula (here) and then solve the resulting quadratic equations?

b) 2x= 4x^3 - 2x^2
Here, the first step is the usual one: getting everything over onto one side of the "equals" sign, with zero on the other side. Then take the common factor out front (here) and then solve the resulting quadratic. Where are you getting stuck?

2. Find all of the zeroes in the following

P(x)= x^4 - 4x^3 - 16x^2 + 21x + 18
"Finding the zeroes" here just means setting the right-hand side equal to P(x) = 0, so you get:

. . . . .\(\displaystyle x^4\, -\, 4x^3\, -\, 16x^2\, +\, 21x\, +\, 18\, =\, 0\)

Then start looking for x-intercepts. It would probably be helpful to try to Rational Roots Test (here) and then start plugging into synthetic division (here), etc, etc. Where are you bogging down?

3. Is (x+2) a factor of x^3 - 3x^2 - 4x
What did you find when you did the long division (here)?

Please be complete. Thank you! ;)
 
Top