solve the equation

Question

express the answers in p and q
x(square) - (p+q)x + (p+1)(q-1)=0
Then x=? or x=?

Answer 1

Recall that in a quadratic equation,
x^2 - (sum of roots)x + (product of roots) = 0
or if we let a & b the roots,
x^2 - (a+b) + (a)(b) = 0

From the given equation, we can see that the constant term is factored, which is (p+1)(q-1). Now, let's assume that the roots are p+1 and q-1. We then check its sum if it is equal to p+q. If it is, then they are the roots of the equation:
p + 1 + q - 1 = p + q
Therefore the roots are p+1 and q+1.

Another way to solve this is to use the quadratic equation:
x = [-b +/- sqrt(b^2 - 4ac)] / 2a
You should get the same answer.

Hope this helps~ :)

Answer 2

*I mean the roots are p+1 and q-1.

Just a typo error. Sorry about that. :3