<p>I believe that was 0 though I’m not sure.</p>
<p>@melzid
if you exand your window you get 6 positive intersections and 2 negative one. expand your xmax to 50…</p>
<p>f(x) not equal to g(x) for at least one value of x
its given that the functions have two distinct roots</p>
<p>The answer was 2,3, and 4 right?</p>
<p>I thought it was 3 and 4 only, but my friend gave the example f(x)=(x+1)(x-1)
and then g(x)=3(x+1)(x-1). Sigh…</p>
<p>@itry why is it not only iii? also, i got -1 for the last one.</p>
<p>@karatekid666
The four positive ones I got were: t=2.6, 9.0, 28.7,30.9. What are the two other positive ones you got?</p>
<p>If it is equal for one value it means they have same root as well</p>
<p>for the f(x)*g(x)=h(x) one i got 3 and 4 solutions bcs you can have (x+1)(x+2) = f(x) and (x+2)(x+3) = g(x) which would yield three solutions and (x+1)(x+2) = f(x) and (x+3)(x+4) = g(x) would be four</p>
<p>@userr u responding to me?</p>
<p>@Nibblin
that’s what i thought, until i realized that ax^3+bx^2 can be factored to x^2(ax+b).
from this, we get the roots of 0 and -b/a, thus, two distinct roots.
if there was an extra x, like cx, then it would be a different story.
goodbye to my 800.
btw, how did you get -1 on the last question?</p>
<p>nvm lol i got it wrong thanks @michial2013</p>
<p>If you look at the example
f(x)=(x+1)(x-1)
g(x)=3(x+1)(x-1)</p>
<p>They are not equal at more than one value and there are only two roots.</p>
<p>@nibblin
I got -1 for the last one, too.
for the f(x)=ax^3+bx^2 one, it is true that the range is all reals (it will approach -infinity one way and +infinity the other) AND it is also true that it has two distinct roots (double-root x=0 and multiplicity-one root x= -b/a). I can’t remember which was I and which was III, but both are true.</p>
<p>@michael it said that the 2 functions could only have 1 of the same roots</p>
<p>@michael2013
what was the question for that? i can’t seem to remember.</p>
<p>ok, 5omit, 1wrong so far…what other problems do u guys remember?</p>
<p>was it one of the same roots or one of the same values?</p>
<p>@melzid
i totally forgot the equations that we were given… do you happen to remember them?</p>
<p>nvm @melzid, i found it… x= 2.65, 9, 15.4, 20, 28.7, 30.85
so the answer was 6</p>
<p>They are equal at more than one value: x=-1 and x=1!</p>
<p>@karatekid666
at 20, the cosine function is 2100 and the exponential funciton is 1966, so the functions don’t intersect at x=20. Check your table of values</p>