sgta101
Question in comments...plz help
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Hawk3ye
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Ok.
sgta101
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\[a^4-29a^2+100<0\]
sgta101
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i really need an explanation or showing of work.
Hawk3ye
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Holy chiznets. What type of math is this. Geometry, Triginometry, Calculus, Algebra, etc.
sgta101
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Algebra
Hawk3ye
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1 or 2
sgta101
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2
sgta101
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quadratic inequalities
Hawk3ye
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Can't help you their. I'm just getting out of Geometry. I take Algebra II starting Tuesday. Sorry laddy.
sgta101
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it's okay, thanks for trying
Hawk3ye
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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!
Hawk3ye
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I gotta kick outta that
sgta101
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im 14 also...
sgta101
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i need to find the solution set of the inequality.
Hawk3ye
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Will you give me a medal for trying?? :DD
sgta101
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Maybe...
RolyPoly
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Can you please solve the quadratic equation first?
I mean to find that value of a when the equation is 0
Hawk3ye
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Tehehe.
sgta101
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ya im pretty sure it's \[a^2-5a-2a+10\]
After it's been factored it's \[(a-5)(a-2)(a-5)(a-2)\]
RolyPoly
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Not quite..
RolyPoly
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No repeated factors in this case.
sgta101
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so just \[(a−5)(a−2)\] ?
RolyPoly
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There are four factors :)
sgta101
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so \[(a−5)(a−2)(a+5)(a+2)\] ?
RolyPoly
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Bingo!
RolyPoly
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|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?
RolyPoly
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*regions
sgta101
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i think i got it from here. one more thing does \[(a^2-5a-2a+10)^2\]
become \[(a^2-7a+10)(a^2-7a+10)\]?
RolyPoly
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Are you still working on the factorization part?
sgta101
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ya im making sure how i got the wrong answer.
sgta101
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i think i messed up in the factorization
RolyPoly
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\[a^4 - 29a^2 +100\]\[=a^4 - 25a^2 - 4a^2 +100\]\[=a^2 (a^2-25) -4(a^2 - 25)\]\[=(a^2-4)(a^2-25)\]\[=(a-2)(a+2)(a^2-25)\]\[=(a-2)(a+2)(a-5)(a+5)\]
The last two steps are just using the identity of difference of two squares.
\(a^2-b^2 = (a+b)(a-b)\)
RolyPoly
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I don't know how you get this:
\[(a^2-5a-2a+10)^2\]
sgta101
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Thanks so much for this. :D
RolyPoly
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You're welcome :)