# Thread: Polynomial and Rational inequalities help

1. ## Polynomial and Rational inequalities help

I have a couple problems I dont understand any help is appreciated..

1.) x^4 - 3x^2 - 4 > 0 solve algebraically.

2.) degree 4: zeros: 3+2i; 4, mulpilicity 2
3.) degree 4: zeros: 3, multiplicity 2; -i

I dont understand 2 and 3 at all, if anyone has any outside sources or good definitions for the problems it would be nice

thanks

2. I'll try to explain this, but it's hard to explain without knowing how much you know already.

For 2 and 3, the degree is the highest power of $x$in the equation, so $x^5$would have degree 5, and $x^5 + x -1$would still have degree 5.

Multiplicity would mean how many times a certain value is makes the equation equal to 0, so $x^2$ would have zeroes at 0 with multiplicity 2, whereas x would only have it with multiplicity 1. you can think of it as being able to factor out zeroes, so for $x^2$ it's the same as x*x, so there's two ways to get 0.

I'm assuming that you want real valued polynomials, so that means that for every complex number you get, it's conjugate is also a zero of the function. A complex number takes the form $x + iy$, and it's conjugate is just $x - iy$.

2.) degree 4: zeros: 3+2i; 4, mulpilicity 2

This means that you have 4 different factors from the degree, so you want to multiply together 4 things that have only degree equal to 1, so it's (x + a) (x+b)(x+c)(x+d) where a, b, c, d are all some value. Now we know that it has to zeroes at 4, so when you plug in 4 you get a 0, which only happens for (x-4). Since the multiplicity is 2, you have this two times. Te other zero is 3+2i, and it's conjugate must also be a zero, so you have 3+2i and 3-2i, which achieve zero at (x-3-2i) and (x-3+2i). Multiply these together: (x-4)(x-4)(x-3-2i)(x-3+2i) and you get your answer.

3. Originally Posted by cokeclassic
I dont understand 2 and 3 at all, if anyone has any outside sources or good definitions for the problems it would be nice
Try reviewing some online lessons regarding how to find quadratics and polynomials from their zeroes.