Finding the Zeros

[Em1313]

Finding the Zeros (Done

I'm having trouble with one of the problems on my makeup work. Can anyone help me? The problem is: f(x)=x³+6x²+12x+8

Thank you sooo much! I'd forgotten how to do these and that helped a lot!

 

[Deleted member 4993]

I'm having trouble with one of the problems on my makeup work. Can anyone help me? The problem is: f(x)=x³+6x²+12x+8

Use rational root theorem first to guess the first root.

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[HallsofIvy]

I'm having trouble with one of the problems on my makeup work. Can anyone help me? The problem is: f(x)=x³+6x²+12x+8

Thank you sooo much! I'd forgotten how to do these and that helped a lot!

If x- a is a factor then x= a must make the function equal to 0. It should be clear that x must be negative and, in order that something like \(\displaystyle (x- a)(x- b)(x- c)= x^3+ 6x^2+ 12x+ 8\), any simple (integer or rational) roots must be divisors of 8. That is the "rational root" theorem that Subhotosh Khan is talking about. There is no guarentee that the roots are integer or rational but cross your fingers and try each of the negative factors of 8 to see if any make that equal to 0. If you can find one, divide by x- a to reduce to a quadratic and then, if nothing simpler, use the quadratic formula to find the other roots.