# SOLVED: The function below has at least one rational zero. Use this fact to find all zeros of the function. h(x)=2x^4-15x^3+7x^2-x+7 If there is more than one zero, separate them with commas. Write ex

Given a Polynomial Function Find All of the Zeros
Given a Polynomial Function Find All of the Zeros

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The function below has at least one rational zero. Use this fact
to find all zeros of the function.
h(x)=2x^4-15x^3+7x^2-x+7
If there is more than one zero, separate them with commas. Write
exact values, not decimal approximations.

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08:27

Find only the rational zeros of the function. If there are none, state this.\$\$f(x)=x^{4}-3 x^{3}-9 x^{2}-3 x-10\$\$

02:58

Find only the rational zeros of the function.\$\$f(x)=x^{4}-3 x^{3}-9 x^{2}-3 x-10\$\$

01:35

Find only the rational zeros of the function.\$\$f(x)=x^{5}-3 x^{4}-3 x^{3}+9 x^{2}-4 x+12\$\$

11:57

Find only the rational zeros of the function. If there are none, state this.\$\$f(x)=x^{5}-3 x^{4}-3 x^{3}+9 x^{2}-4 x+12\$\$

01:40

Find only the rational zeros of the function.\$\$f(x)=x^{3}-x^{2}-4 x+3\$\$

Transcript

the key to this problem is using the rational root theorem as well as synthetic Maybe two X. to the 4th -15. x cubed Plus seven, x squared -X. And then plus seven. So the rational root theorem says is the possible rational roots. I like to write P R. R. Are the positive and negative factors of the constant positive negative one positive negative seven. But you also want to consider factors of the leading coefficient because of what could also happen is um you know, factors of the seven divided by factors of the leading coefficient. But doing a little bit of the investigation and this is how I set up synthetic. I don’t know if your teacher does a little bit differently but if you get a remainder of zero then what you trying your problem is a root. Um So I did an investigation so that one works because as I do my synthetic where I add straight down and multiplied by what’s in the box. two times 1 is to again add straight down negative 15 plus two is negative…

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