Expert: David Hemmer - 5/13/2007

Question
Hello Mr. Hemmer.

I need some help with some homework.  Yes, you're going to be doing my homework...haha...if you don't mind.  I was actually quite good at math when I was in college years ago.  I'm 37 now and taking a math course again.

I've done almost all of them, but these I am stuck on.  Would you mind helping me with these last few?  Thanks.  They are as follows:

1) Use the discriminant to classify the solutions of 2xsquared + 5x + 5 = 0
2) Write the equations whose solutions are -4 or 3
3) Find the real solutions to each equation
  a) x to the one half power - 8x to the one quarter power + 15 = 0
  b) the quanity (x squared - x)squared - the quantity (x squared - x) - 30 = 0
4) Solve inequality.  Write solution in interval notation
  x squared - 3x - 4 < 0

And, you don't have to write all steps.  Some intermediate steps to show how would be appreciated.  Thanks!!

Answer
1. THe discriminatnt is b^2-4ac which in this case is -15 so there are no real roots, two imaginarys solutions.

2. (x+4)(x-3)=0, aka x^2+x-12=0.

3. a. Let w=x^1/4. Then your equation turns into w^2-8w+15=0. This has solutions w=5, w=3. Thus x=625 or 81.

b. As in 3a, let w=x^2-x. Then solve w^2-w-30=0 for w. THen solve for x.

4. First set it =0 to get x=4, x=-1. Then do test points. Your answer will be (-1,4).