[bosey]

Help! I need to find the answer to the following two questions by 4:00 p.m. today. Any assistance you can provide will be greatly appreciated!

Polynomial and Rational Inequalities:

Problem: Solve : x^2 + 56 < 15x


Equations Quadratic in Form:

Problem: Solve: x^4 - 10x^2 +25 = 0

[dmatos]

Well, it's 9:30, so I'm guessing you missed your deadline or already figured this out. But, in case you still need some help (though I'm not going to do your homework for you), these questions are both about factoring.

x^2 + 56 < 15x

Step 1: rearrange so that all terms are on one side of the equation
Step 2: factor to a form (x-a)(x-b)<0
Step 3: solve (x-a)(x-b)=0
Step 4: this should divide values of x up into three different domains - greater than b, less than a, and between a and b. Now figure out in which of these domains the original inequality holds true. It can be one, two, or all three of them.

x^4 - 10x^2 + 25 = 0

Step 1: let y = x^2, that means y^2=x^4. Make these substitutions
Step 2: factor the quadratic equation, and solve for all possible answers for y
Step 3: take your equations y=a and y=b, and substitute x^2 back in for y
Step 4: solve for all possible values of x

Cheers!