consecutive integers can be represented as x an x+1
thei poduct is 30
so (x)(x+1)=30
[tex]x^2+x=30[/tex]
[tex]x^2+x-30=0[/tex]
use quadratic formula
for [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
for ours, a=1, b=1, c=-30
[tex]x=\frac{-1 \pm \sqrt{1^2-4(1)(-30)}}{2(1)}[/tex]
[tex]x=\frac{-1 \pm \sqrt{121}}{2}[/tex]
[tex]x=\frac{-1 \pm 11}{2}[/tex]
[tex]x=\frac{-1+11}{2}[/tex] or [tex]x=\frac{-1-11}{2}[/tex]
x=(10/2) or x=-12/2
x=5 or x=-6
for x=5
x+1=6, the integers are 5 and 6
or x=-6
x+1=-5, the integers are -6 and -5
the integers are 5 and 6 or -5 and -6 (the question didn't say anything about the signs of the integers)
