Please Help me about integral expression >_<

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 >_<

Re: Please Help me about integral expression >_<

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.

Re: Please Help me about integral expression >_<

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

Re: Please Help me about integral expression >_<

Quote:

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?

Re: Please Help me about integral expression >_<

Quote:

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...

Re: Please Help me about integral expression >_<

Quote:

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!

Re: Please Help me about integral expression >_<

oh thank you I didn't noticed it since I am always focus at the first given problem >_<

Re: Please Help me about integral expression >_<

Quote:

Originally Posted by

**sarcosuchus** At a=? the value of P is a rational number for any x which satisfies the equation x^2 + 2x -2=0,

Huh? Sure was part of the given problem...