Determine an equation of p(x)

  • Thread starter Nelo
  • Start date
In summary, eumyang said that the equation for the family of quartic functions with zeroes is x^4- 8x^3+ 16x^2+ 64x- 100.
  • #1
Nelo
215
0

Homework Statement



Determine the equation in simplied form for the family of quartic functions with zeroes of..

5 (order 2) and -1± 2√ 2



Homework Equations





The Attempt at a Solution



so.. (x-5)^2 (x-1+2√2) (x-1-2√2)

(x-5) (x-5) (x-1+2√2) (x-1-2√2)

Would be all of it expanded, but I don't know how to foil on this.. there's 2 terms on the left side brackets and 3 terms on the right side brackets.. (x) (-1) (2√2) , I know that X will become x^4, but i don't get how to continue using foil, can anyone explain?

We never learned this.. so.. i also know that the plusminus root is (x+1)^2 + 8 if simplified into that form..
 
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  • #2
Nelo said:
so.. (x-5)^2 (x-1+2√2) (x-1-2√2)
This is wrong. It should be
(x - 5)^2 [x - (-1+2√2)][x - (-1-2√2)]
= (x - 5)(x - 5)[x + 1 - 2√2][x + 1 + 2√2]

Nelo said:
Would be all of it expanded, but I don't know how to foil on this..
FOIL the first two binomials, and then FOIL the last two binomials. In FOILing the last two binomials, it may be helpful to rewrite like this:
[x + 1 - 2√2][x + 1 + 2√2]
= [(x + 1) - 2√2][(x + 1) + 2√2]
.. and then use the sum+difference pattern (a - b)(a + b) = a2 - b2.

Then, multiply the two resulting trinomials (see http://www.purplemath.com/modules/polymult3.htm" [Broken] if you don't know how).

Nelo said:
We never learned this.. so.. i also know that the plusminus root is (x+1)^2 + 8 if simplified into that form..
This is also wrong (probably because you were missing signs earlier. It should be
(x+1)^2 - 8.
 
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  • #3
wat? explain... why are you distributing random negetives into those brackets
 
  • #4
Nelo said:
wat? explain... why are you distributing random negetives into those brackets
Because if a is a root of a polynomial equation f(x) = 0, then
(x - a)
is a factor of that polynomial. So there is a negative outside the roots -1+ 2√ 2 and -1 - 2√ 2:
(x - 5)(x - 5)[x - (-1 + 2√ 2)][x - (-1 - 2√ 2)]
 
  • #5
okay..? so you factor inwards...? like (x+1 -2√ 2) and (x+1 +2√ 2) ?
 
  • #6
any1?
 
  • #7
Nelo said:
okay..? so you factor inwards...? like (x+1 -2√ 2) and (x+1 +2√ 2) ?
What do you mean by "factor inwards" ?

Also, eumyang basically gave you the next step.
 
  • #8
The simplest thing to do with complex conjugate terms is to use [itex](a- b)(a+ b)= a^2- b^2[/itex].

If [itex]-1+ 2\sqrt{2}[/itex] and [itex]-1- 2\sqrt{2}[/itex] then [itex](x- (-1+2\sqrt{2})[/itex] and [itex](x- (-1-2\sqrt{2}))[/itex] are factors.

[tex]((x- 1)- 2\sqrt{2})((x-1)+ 2\sqrt{2})= (x- 1)^2- (2\sqrt{2})^2= x^2- 2x+ 1- 8= x^2- 2x- 7[/tex].

It shouldn't be too difficult to multiply [itex](x^2- 10x+ 5)(x^2- 2x- 7)[/itex]
 

1. What does it mean to "determine an equation of p(x)"?

Determining an equation of p(x) means finding an algebraic expression that represents a relationship between the independent variable, x, and the dependent variable, p(x). This equation can then be used to calculate the value of p(x) for any given value of x.

2. How do you determine an equation of p(x) from a table of values?

To determine an equation of p(x) from a table of values, identify the pattern or relationship between the x-values and the corresponding p(x) values. Then, use this pattern to write an equation in the form of p(x) = mx + b, where m is the slope and b is the y-intercept.

3. What are the different types of equations of p(x)?

The different types of equations of p(x) include linear, quadratic, exponential, logarithmic, and trigonometric equations. Each type has a unique form and can be used to model different relationships between x and p(x).

4. Can you determine an equation of p(x) without a given table of values?

Yes, it is possible to determine an equation of p(x) without a given table of values. This can be done by using other information, such as the graph or a verbal description of the relationship between x and p(x), and applying algebraic techniques to find the equation.

5. How can determining an equation of p(x) be useful in science?

Determining an equation of p(x) can be useful in science as it allows us to model and predict the behavior of a variable, p(x), based on changes in the independent variable, x. This can help in understanding and analyzing scientific data, making predictions, and developing theories and hypotheses.

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