## [SOLVED] polynomial with two unknowns

1. The problem statement, all variables and given/known data
The graph of f(x)= 3x^4 + 14x^3 + px^2 + qx + 24 has x-intercepts -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: 2p-q=13.3
Don't know what to do next.
 Rather then setting them equal to each other. Solve for p with one of your x-intercepts then plug it in your other set with the other x-intercept.
 but there are two unknowns in each expression

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## [SOLVED] polynomial with two unknowns

 Quote by AFG34 but there are two unknowns in each expression
What roco is getting at is that you can create a system of two simultaneous equations thus;

$$f(-4) = 0$$

$$f(2) = 0$$
 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.

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 Quote by AFG34 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.
Have you never solved simultaneous equations before?
 no, i haven't.

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 Quote by AFG34 i don't think so.
Okay, in that case if you post the two equations you obtain I shall walk you through the process.
 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
 Blog Entries: 1 Recognitions: Gold Member Science Advisor Staff Emeritus Good, so now multiply (2) by 2 and then add the two equations.
 Did you ever learn to solve matrices in Algebra class?
 8p + 132 ok so p = -11, q = -70 thnx

 Quote by rocophysics Did you ever learn to solve matrices in Algebra class?
nope

 Quote by AFG34 nope

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

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