My teacher gave us a problem and I cannot understand how did she do it >_< it is about integral expression I am really weak at mathematics even I focus it takes time for me to understand the topic but she is very fast when teaching I hope you can help me I didn't even have any idea what is integral expression she gave us this problem
consider the integral expression in x
P=x^3 + x^2 + ax + 1
where a is a rational number, At a=? the value of P is a rational number for any x which satisfies the equation x^2 + 2x -2=0, and in this case the value of P =?
and the answer is a=-4 p=-1
how she do it and what is integral expression I am very sorry >_<

Find the roots of x^2 + 2x - 2 = 0, substitute them into x^3 + x^2 + ax + 1 and see when the resulting expression of a is rational.

thank you but where did you get x^2 + 2x -2 = 0?

Originally Posted by sarcosuchus
thank you but where did you get x^2 + 2x -2 = 0?
Hmm, have you fully read the text of the problem?

Originally Posted by sarcosuchus
My teacher ... but she is very fast when teaching...
....the equation x^2 + 2x -2=0,
You seem to be "very fast" when reading...

Originally Posted by sarcosuchus
thank you but where did you get x^2 + 2x -2 = 0?
The point is that you said, in the problem, "for any x which satisfies the equation x^2 + 2x -2=0". That's where emakarov got it!