- #1
Theofilius
- 86
- 0
Homework Statement
Find polynoms, with as least as power possible, so they will be competent for the equation.
[tex](x^4+2x^3+x+1)A(x) + (x^4+x^3-2x^2+2x-1)B(x)=x^3-2x[/tex]
Theofilius said:I mean, if it is [tex]x^100 + x^99[/tex], aren't any fixed way? If not its ok.
Theofilius said:Sorry, I meant if there any 100% way sure, is there any fixed way, so I can solve the equation withouth trying?
Theofilius said:Sorry, if I am misunderstud. I want to know is there any fixed principle for solving this equation? If not, its ok. In which form will be A(x). [tex]A(x)=ax^2+bx+c[/tex]. What about B(x)?
tiny-tim said:Hi Theofilius and Physicsissuef!
The solution is:
[tex]A(x)\,=\,(3x^3\,+\,3x^2\,-\,7x\,+\,2)\,;\,B(x)\,=\,(-3x^3\,-6x^2\,+\,x\,+\,2)\,.[/tex]
But the way I go it is fairly horrible , so I'm going to carry on thinking about it - I'm sure there must be a simpler way!
Theofilius, what did they teach you in class about remainders? Maybe there's a clue in there somwehere …
Physicsissuef said:What way you were using? Is my way, correct?
Physicsissuef said:Are you talking about the polynom that Theofilius had given, or this is yours polynom?
Physicsissuef said:Can you please start from beginning and write the problem without using latex. Why you used 1/A-B and 1/A+B, and so on... Please!