## sgta101 2 years ago Question in comments...plz help

1. Hawk3ye

Ok.

2. sgta101

\[a^4-29a^2+100<0\]

3. sgta101

i really need an explanation or showing of work.

4. Hawk3ye

Holy chiznets. What type of math is this. Geometry, Triginometry, Calculus, Algebra, etc.

5. sgta101

Algebra

6. Hawk3ye

1 or 2

7. sgta101

2

8. sgta101

9. Hawk3ye

Can't help you their. I'm just getting out of Geometry. I take Algebra II starting Tuesday. Sorry laddy.

10. sgta101

it's okay, thanks for trying

11. Hawk3ye

I aced Algebra I though I know that much. In my day we didn't have all this fancy schmancy stuff(I'm only 14). I don't know nuttn bout dis der Aljero!

12. Hawk3ye

I gotta kick outta that

13. sgta101

im 14 also...

14. sgta101

i need to find the solution set of the inequality.

15. Hawk3ye

Will you give me a medal for trying?? :DD

16. sgta101

Maybe...

17. RolyPoly

Can you please solve the quadratic equation first? I mean to find that value of a when the equation is 0

18. Hawk3ye

Tehehe.

19. sgta101

ya im pretty sure it's \[a^2-5a-2a+10\] After it's been factored it's \[(a-5)(a-2)(a-5)(a-2)\]

20. RolyPoly

Not quite..

21. RolyPoly

No repeated factors in this case.

22. sgta101

so just \[(a−5)(a−2)\] ?

23. RolyPoly

There are four factors :)

24. sgta101

so \[(a−5)(a−2)(a+5)(a+2)\] ?

25. RolyPoly

Bingo!

26. RolyPoly

|dw:1358566081932:dw| So, the graph is like this (sorry for my poor drawing..) In what region does the function have a value less than 0?

27. RolyPoly

*regions

28. sgta101

i think i got it from here. one more thing does \[(a^2-5a-2a+10)^2\] become \[(a^2-7a+10)(a^2-7a+10)\]?

29. RolyPoly

Are you still working on the factorization part?

30. sgta101

ya im making sure how i got the wrong answer.

31. sgta101

i think i messed up in the factorization

32. RolyPoly

\[a^4 - 29a^2 +100\]\[=a^4 - 25a^2 - 4a^2 +100\]\[=a^2 (a^2-25) -4(a^2 - 25)\]\[=(a^2-4)(a^2-25)\]\[=(a-2)(a+2)(a^2-25)\]\[=(a-2)(a+2)(a-5)(a+5)\] The last two steps are just using the identity of difference of two squares. \(a^2-b^2 = (a+b)(a-b)\)

33. RolyPoly

I don't know how you get this: \[(a^2-5a-2a+10)^2\]

34. sgta101

Thanks so much for this. :D

35. RolyPoly

You're welcome :)