Question 427099
I would use the discriminant :
That is for ax^2+bx+c=0
the discriminant is b^2-4ac
a=1, b=7, c=12
b^2-4ac={{{7^2-4*1*12=49-48=1}}}
the zeros are for {{{(-7+-sqrt(1))/(2*1)}}}=(-7+-1)/2
{{{a[1]=-3}}} {{{a[2]=-4}}}
Factorize:
{{{(a-(-3))(a-(-4))=0}}}
{{{(a+3)(a+4)=0}}}.
You may also write directly
{{{a^2+3a+4a+12=0}}}
{{{a(a+3)+4(a+3)=0}}}
{{{(a+3)(a+4)}}}=0
so
a+3=0 or a+4=0
That is
a=-3 or a=-4