math (Algebra)
posted by Help generation .
Express x2+4x+7 in the form (x+p)2+q. Hence show that equation x2+4x+7=0 has no real root???...I have problem in writing square in my computer so remember x2 is x square and 2 after bracket is squarer too.

the usual way to write powers in this forum is x^2 for x^{2}
so x^2 + 4x + 7
= x^2 + 4x + 4  4 + 7
= (x+2)^2 + 3
If I had the parabola y = (x+2)^2 + 3
its vertex would be above the xaxis at (2,3) and it opens upwards.
So it cannot cross the xaxis.
Since roots are simply the xintercepts of the corresponding function, we conclude that there are no real roots.