# Polynomial with two unknowns

by AFG34
Tags: polynomial, solved, unknowns
 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 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.
 P: 1,754 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.
 P: 128 but there are two unknowns in each expression
Emeritus
PF Gold
P: 9,772
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;

$$f(-4) = 0$$

$$f(2) = 0$$
 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.
Emeritus
PF Gold
P: 9,772
 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?
 P: 128 no, i haven't.
Emeritus
PF Gold
P: 9,772
 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.
 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
 Emeritus Sci Advisor PF Gold P: 9,772 Good, so now multiply (2) by 2 and then add the two equations.
 P: 1,754 Did you ever learn to solve matrices in Algebra class?
 P: 128 8p + 132 ok so p = -11, q = -70 thnx
P: 128
 Quote by rocophysics Did you ever learn to solve matrices in Algebra class?
nope
P: 1,754
 Quote by AFG34 nope

I'll go step by step. Let me type this up.
Emeritus
PF Gold
P: 9,772
 Quote by rocophysics Did you ever learn to solve matrices in Algebra class?
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).
 Quote by AFG34 8p + 132 ok so p = -11
Firstly, what you have written is an expression, not an equation. Secondly, you might want to check your coefficent of p.
 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
P: 1,754
 Quote by AFG34 0 = 12p + 132 is an equation ya i typed it wrong checked the back of the book, got the right answer. ok i know how to do them now, thnx
Want to learn the fast way?
 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.

 Related Discussions Calculus & Beyond Homework 5 Calculus & Beyond Homework 2 Introductory Physics Homework 13 Precalculus Mathematics Homework 11 Precalculus Mathematics Homework 12