[SOLVED] polynomial with two unknowns

AFG34

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.

rocomath

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.

AFG34

but there are two unknowns in each expression

Hootenanny

What roco is getting at is that you can create a system of two simultaneous equations thus;

[tex]f(-4) = 0[/tex]

[tex]f(2) = 0[/tex]

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.

Hootenanny

Have you never solved simultaneous equations before?

AFG34

no, i haven't.

Hootenanny

Okay, in that case if you post the two equations you obtain I shall walk you through the process.

AFG34

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

Hootenanny

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

rocomath

Did you ever learn to solve matrices in Algebra class?

AFG34

8p + 132

ok so p = -11, q = -70

thnx

AFG34

nope

rocomath

Well either way, your answer isn't right b/c your answer should have ended up being in terms of a solution.

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

Hootenanny

If the OP hasn't met simultaneous equations it's pretty safe to say that they haven't been introduced to linear algebra (which IMHO is over-kill for a question such as this).
Firstly, what you have written is an expression, not an equation. Secondly, you might want to check your coefficent of p.

AFG34

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

rocomath

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