Solving Polynomials - Answers to Common Questions

  • Thread starter Thread starter Kyoma
  • Start date Start date
  • Tags Tags
    Polynomials
AI Thread Summary
To solve the polynomial equation x^5 + ax^3 + bx^2 - 3 = (x^2 - 1)Q(x) - x - 2, substitute x = 1 and x = -1 to eliminate Q(x) and create two equations involving a and b. This approach allows for simultaneous solving of the equations to find the values of a and b. A similar method can be applied to the second equation, 4x^3 + 5x - 2 = (x + 2)(x - 1)P(x) + ax + b, by choosing specific values of x that simplify the equation and eliminate P(x). The key is to strategically select x values that make certain terms zero, facilitating the solution process. Understanding these techniques is crucial for solving polynomial equations effectively.
Kyoma
Messages
95
Reaction score
0
i'm pretty new to polynomials and I have qns, which I do not know how to solve.

x5 + ax3 + bx2 - 3 = (x2 - 1)Q(x)- x - 2

Q(x) is a polynomial. Solve a and b.

I know the degree of Q(x) is 3, so I subst Q(x) into x3, but I got stuck.

Help. Thanks in advance.
 
Physics news on Phys.org
You don't need to know what Q(x) is. The zeroes of x^2-1 are x=\pm 1 so if you substitute x=1 into the entire equality, that Q(x) part cancels since anything times zero is zero (your 'anything' is the Q(x)) and then you'll get an equation in a and b. Then substitute the other value of x to get another equation in a and b. Solve simultaneously and you're done! :smile:
 
Thank you very much.

How about this:

4x3 + 5x - 2 = (x+2)(x-1)P(x) + ax + b

Find a and b. Last qns, I seriously can't solve!
 
If you thought a bit more about what I posted you should have picked up on what to do. What values of x can you choose so that you eliminate the P(x)?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Roots of a polynomial mixed with a trigonometric function
Replies
14
Views
2K
Questions about proof of upper and lower bound theorem for polynomials
Replies
11
Views
2K
Finding Solutions for Polynomial Division: Where to Begin?
Replies
22
Views
3K
I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
Replies
48
Views
3K
Prove: polynomial is uniquely defined by three of its values
Replies
2
Views
2K
A Have I solved this iterative equation correctly?
Replies
2
Views
217
Remainder factor theorem: me reason this out
Replies
33
Views
4K
Iterative root finding for the cube root of 17
Replies
3
Views
4K
Engineering Have I solved this structural engineering equation correctly?
Replies
0
Views
155
Finding values for a and b for this polynomial
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top