<p>hi all. just wondering if you could help me solve these 2 problems/tell me how to go about solving them.</p>
<p>find the zeros of f(x).</p>
<p>f(x)=-3x^-2 + 8x^-3 + 12x^-4</p>
<p>f(x)= (e^x^2 - 2x(x-1)e^x^2)/ (e^2x^2)</p>
<p>Geez - I hope these aren't SAT problems, lol!</p>
<p>I would combine terms in the first one by multiplying to get x^4 as a common denominator - you end up with:
(-3 x^2 + 8x + 12)/ x^4
Since the denominator cannot = zero, you are left with getting the zeros by making the numerator = 0. So use the quadratic (or completing the square) to get to the final roots of:
(4 +/- 2sqrt(13))/3) </p>
<p>Second one - factor out e^(x^2) to get
(e^(x^2) (1-2x^2+2x) ) / e^(x^2)
then the e's cancel to give you:
(-2x^2 + 2x +1) which you have to set = 0 and solve again by the quadratic or completing the square to get</p>
<p>(1 + sqrt (3))/2</p>
<p>I did these super fast so you have to do to the work yourselved to verify the math (he,he,he)</p>
<p>Couldn't you put them in the graph function of a graphing calculator, then see where they intersect the x-axis?</p>
<p>ABlestMom, you are good at math.</p>
<p>ok. First of all, the easiest way to do it is to graph it like coldeggnog suggested and find the x-intercepts. Personally, I would solve them using derivatives, then setting the equations to 0 and solving. (Only because I can, and too lazy to do it using algebra(?))</p>
<p>Akai:
Setting the derivatives to 0 will give you the max/min points of f(x), not the solution for f(x)=0 . AblestMom had it right.</p>
<p>One word: TI-89. Done in 15 seconds.</p>
<p>hahah yeah for sure i agree with GDWilner</p>
<p>Problem is - I felt sure it's an algebra problem that needed to show a worked out solution versus a quick answer solution - which is why I showed it the long way.</p>
<p>Thanks evanescenteuphoria :) I'm a math & science h.s. & college tutor</p>
<p>Good going optimizerdad - a mathematician perhaps, lol!</p>
<p>AblestMom, Optimizerdad's screenname gives it away. </p>
<p>OD has a knack for giving us great mathematical solutions. I suspect he feeds the problem into the Craig computer he refurbished and installed in his basement to run his optimization models. :)</p>
<p>By the way, I like the double entendre of the SN: Ablest (of) Moms or A Blessed Mom. Please continue to show complete solutions.</p>
<p>you're absolutely right optimizerdad!</p>
<p>Xiggi:
Curses, unmasked again. But you didn't mention the punched cards I have to feed to that brute... :)</p>
<p>Thanks Xiggi - LOVE your SAT insight!!!</p>
<p>Optimizerdad:
aaahhhhh punched cards (fingers crossed to ward away evil)</p>