maths
posted by Jayden Haddy on .
If the roots of x^2  px + q = 0 are two consecutive integers, prove that p^2  4q 1 = 0

sum = p
product = q
let a & b the roots
a + b = p
ab = q
since a & b are consecutive integers (i.e. b = a+1):
2a + 1 = p
a^2 + a = q
substitute.
p^2  4q 1 = 0
4a^2 + 4a + 1  4a^2 + 4a  1 = 0
indeed,
0 = 0