Thread: Two problems

For what value on "a" has the equation an infinite amount of solutions?

For a quadratic polynomial:



What is the polynomial p(x).

I don't want the answers to these questions, I simply would like some help with them. As I don't know where to start with either of them.

EDIT: I believe that I have managed to solve the first problem. I'd like to know if it's a valid solution.

"[unparseable or potentially dangerous latex formula]"

Hopefully this will suffice.

(x^2+2x+1)^2 = (x+a)^4
(x^2+2x+1) = (x+a)^2
(x+1)^2 = (x+a)^2
(x+1) = (x+a)
1 = a

For the second problem you need to use a method call "synthetic division"

http://www.purplemath.com/modules/synthdiv.htm

http://mathworld.wolfram.com/SyntheticDivision.html

Above are a couple of websites which give details. If you google "synthetic division" you can get a lot more.

Originally Posted by mathman

For the second problem you need to use a method call "synthetic division"

Thank you for your reply, and the links. I had a look at both the websites, but I'm not quite sure how to apply the method to the problem addressed in my question.

p(x)=(x^3 + x - 2)/(x - 1)

Step 1a: x^2 = x^3/x
Step 1b: (x^3 +x - 2)-x^2(x - 1) = x^2 + x - 2
Step 2a: x=x^2/x
Step 2b: (x^2 + x - 2) -x(x - 1)= 2x - 2 = 2(x-1)
(I have elided the last step, because of the obvious factor of (x - 1).)

Final answer p(x) = x^2 + x + 2