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sabika13
Group Title
The graph of f(x) = ax^4 + bx^2 + cx24 crosses the xaxis at 1, 2, and 3. determine the equation of f(x).
 2 years ago
 2 years ago
sabika13 Group Title
The graph of f(x) = ax^4 + bx^2 + cx24 crosses the xaxis at 1, 2, and 3. determine the equation of f(x).
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
start with \[(x1)(x+2)(x3)(xr)\] and see if you can solve for \(r\)
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
do i expand and then solve?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
no you don't really have to expand yet, you can visualize what the constant should be the constant will be \(6r\) so you know \(6r=24\) and if you are lucky \(r=4\) works
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
oh damn it doesn't because you get a cube term and your polynomial doesn't seem to have one
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
on the other hand something is wrong, because you have a 4th degree polynomial. it has 4 zeros total, although either two or four could be complex. however, if it crosses the \(x\) axis 3 times it must cross it a fourth. if one root is repeated, then it does not cross the axis but only touches it. so i am stumped
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
maybe one passes through origin?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then it still has 4 zeros one would be zero, and also it could not end in \(24\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it really starts with \(ax^4\) right?
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
i have the answer if that helps?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
ok i am very certain that a fourth degree polynomial cannot cross the \(x\) axis only 3 times
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
sure go ahead and let me see why i am wrong
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
its f(x)= 4x^3 + 8x^2 + 20 x 20
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
we could perhaps start with \[a(x1)(x+2)(x3)(xr)\] and see if we can solve for the coefficients, but it must cross 4 times
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
f(x)= 4x^3 + 8x^2 + 20 x 24 *** sorrry
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
hold the phone, it is cubic?
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
the answers a cubic :S
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i thought it was a 4th degree polynomial, since you wrote \[f(x) = ax^4 + bx^2 + cx24\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if it is \[f(x) = ax^3 + bx^2 + cx24\] then that is a whole different story
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
lol thats what the question says, its ax^4 + bx^2 ..
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
and much simpler write \[a(x1)(x3)(x+2)= ax^3 + bx^2 + cx24\] and solve
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then there is something wrong with the question, it is a typo
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
so if its ax^3 will the answer be right?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
your question asks for a 4th degree polynomial, which must have 4 zeros. it also has no cube term your answer has a third degree polynomial, so there is a mistake in the question
 2 years ago

sabika13 Group TitleBest ResponseYou've already chosen the best response.0
yeah it prob is a typo.. ah been trying to question for so long.. thanks tho!
 2 years ago
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