This is an example question and I am confused on how they solved the question. It's lesson tittle is solving quadratics by factoring.
x^2-7x+12=0
x=3 and x=4

Question

This is an example question and I am confused on how they solved the question. It's lesson tittle is solving quadratics by factoring.
 x^2-7x+12=0 
x=3 and x=4

anonymous · Answer

if we take some generic factors:

(x+a)(x+b)  and multiply them together, what do we get?

anonymous · Answer

x^2 +ab right??

anonymous · Answer

(x+a)(x+b) ... if FOIL rings a bell:  x^2 +ax + bx + ab

so:  x^2 + (a+b)x + ab, has to equal, x^2 -7x + 12

in order for these to be the exact same thing, then:
      a+b = -7
         ab = 12

anonymous · Answer

since 12 is a positive number,  a,b are the same sign
since -7 is negative, the signs of a,b have to be negative

what are the factors of 12?

1,12 .. adds to 13
2,6   .. adds to 8
3,4   .. adds to 7, this has to be the correct set then

anonymous · Answer

so, let a = -3,  and b = -4

the roots are then, -3, -4