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Polynomial with two unknowns 
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#1
Jan2608, 05:44 PM

P: 128

1. The problem statement, all variables and given/known data
The graph of f(x)= 3x^4 + 14x^3 + px^2 + qx + 24 has xintercepts 4 and 2. Determine the function. 3. The attempt at a solution I could solve it if there were only one unknown but i don't know how to do it if there are two unknowns. What i did so far is plug 4 for x and 0 for the output, got an expression = 0 did the same thing for 2 since both equal 0, i set them equal to each other, simplified and got: 2pq=13.3 Don't know what to do next. 


#2
Jan2608, 06:09 PM

P: 1,754

Rather then setting them equal to each other. Solve for p with one of your xintercepts then plug it in your other set with the other xintercept.



#3
Jan2608, 07:17 PM

P: 128

but there are two unknowns in each expression



#4
Jan2608, 07:21 PM

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P: 9,772

Polynomial with two unknowns
[tex]f(4) = 0[/tex] [tex]f(2) = 0[/tex] 


#5
Jan2608, 07:28 PM

P: 128

yes i know that, that is what i initially did. So you get 2 equations, both equal to 0, both have q and p in them. But i don't know what to do next.



#6
Jan2608, 07:29 PM

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PF Gold
P: 9,772




#7
Jan2608, 07:32 PM

P: 128

no, i haven't.



#8
Jan2608, 07:33 PM

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P: 9,772




#9
Jan2608, 07:36 PM

P: 128

1) 0 = 16p  4q  104
2) 0 = 4p +2q + 184 then i divided both by 2: 1) 0 = 8p  2q  52 2) 0 = 2p + q + 92 


#10
Jan2608, 07:43 PM

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P: 9,772

Good, so now multiply (2) by 2 and then add the two equations.



#12
Jan2608, 07:47 PM

P: 128

8p + 132
ok so p = 11, q = 70 thnx 


#13
Jan2608, 07:49 PM

P: 128




#14
Jan2608, 07:52 PM

P: 1,754

I'll go step by step. Let me type this up. 


#15
Jan2608, 07:55 PM

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P: 9,772




#16
Jan2608, 08:36 PM

P: 128

0 = 12p + 132 is an equation
ya i typed it wrong checked the back of the book, got the right answer (f(x)= 3x^4 + 14x^3  11x^2  70x + 24). ok i know how to do them now, thnx hootenanny, funny name 


#18
Jan2608, 09:22 PM

P: 128

sure
got a quick question: is the graph of y = log3^(x+4) the same as the graph of y = log3^x+4? *the base is 3 not 10 I think the second one is y=log3^x moved up by 4 units. 


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