we are given
[tex] a^2+5a+6=0 [/tex]
we can use factoring formula
[tex] a^2-(m+n)a+mn=(a-m)(a-n) [/tex]
we can compare
and we get
[tex] m+n=-5 [/tex]
[tex] mn=6 [/tex]
now, we can solve for m and n
and we get
[tex] m=-3 , n=-2 [/tex]
now, we can use formula
and we get
[tex] a^2+5a+6=(a+3)(a+2) [/tex]
now, we can set it equal to 0
[tex] a^2+5a+6=(a+3)(a+2)=0 [/tex]
[tex] (a+3)=0 [/tex]
[tex] a=-3 [/tex]
[tex] a+2=0 [/tex]
[tex] a=-2 [/tex]
so, we will get
[tex] a=-2,a=-3 [/tex].............Answer
You did a good job of sharing this quadratic equation in proper symbolic notation, but you haven't yet shared the instructions for this problem.
I will assume that you are to find the roots / zeros of a^2+5a+6=0. Factoring results in (a+3)(a+2)= 0, from which we deduce that a = -3 and a = -2.
The solution set is {-3, -2}.
