Zeros in Function: g(x) = x^3 + 6x^2 + 21x + 26, etc

[Emanual]

Find all of the zeros of each function.

g(x) = x^3 + 6x^2 + 21x + 26

h(x) = 4x^4 + 17x^2 + 4

g(x)= 2x^3 - x^2 + 28 + 5

f(x) = x^3 - 5x^2 - 7x + 51

This have been some trouble I am not sure what do, and need some help. Can some one show me how to find the answers step by step and explain.

Thanks in advance for the help.

 

[galactus]

Re: Zeros in Function

I will help with one of them, Emanuel. You try the others and write back if you're hung up. OK?.

\(\displaystyle h(x) = 4x^{4} + 17x^{2} + 4\)

Rwrite as \(\displaystyle \L\\4x^{4}+16x^{2}+x^{2}+4\)

Now factor: \(\displaystyle \L\\4x^{2}(x^{2}+4)+(x^{2}+4)\)

\(\displaystyle \L\\=(4x^{2}+1)(x^{2}+4)\)

Now, to find the zeros, what makes \(\displaystyle 4x^{2}+1=0\) and what makes \(\displaystyle x^{2}+4=0\)?.

I will give you a big hint; They're all complex.

 

[Emanual]

What did you do to get that?

Rewrite as \(\displaystyle \L\\4x^{4}+16x^{2}+x^{2}+4\)

 

[galactus]

What did I do to get that?. My heaven's, you are in trouble. 16+1=17,doesn't it?.

 

[Emanual]

Why is there another x^2? and what did you substitute with the number 1?

 

[galactus]

You need much more help than I can give. Maybe you should see your instructor.