a maths - quadratic inequalities

bonkysleuth SG

given that p, q and r are non zero real numbers, prove that the roots of the quation (x-p)(x-q) = r^2 are real and different.

i expanded out the equation and found the discriminant. it is (-q-p)^2 -4(pq - r^2). can i prove from here that the roots are real and different?

eagle SG

(x-p)(x-q) = r^2
x² - (p+q)x + (pq-r²) = 0

discriminant = (-p-q)² - 4(1)(pq-r²)
= (p+q)² - 4(pq - r²)
= p² +2pq + q² - 4pq + 4r²
= p² - 2pq + q² + 4r²
= (p - q)² + 4r²

Since p, q and r are non zero real numbers,
(p - q)² + 4r² > 0
discriminant > 0

hence, the roots are real and different