Question

The product of two consecutive integers is 420. Which quadratic equation can be used to find x, the lesser number?

Answer 1

(x) * (x+1) = 420
x^2 +x = 420
x^2 +x -420 = 0
a = 1
b=1
c=-420

x = -b +-sq root(b^2 -4*a*c) / (2*a)
x = -1 +-sq root(1 -4*1*-420) / (2*1)
x = [-1 +-sq root(1 +1680)] / 2
x = -1/2 +- 41/2
x1 = 20
x2 = -21

So, the numbers are 20 and 21
and -21 and -20