3x^2 + 11x -4=0
ax^2 +bx +c=0
Multiply ac to get -12
find factors the multiply to get -12 and add to get the coefficient of the middle term +11
Because we want -12, one factor is negative and the other is positive. Because we want the sum to be +11, the factor with greater absolute value is the positive factor:
List:
-1xx12 sum -1+12 = 11 STOP!, that's the one we want.
Now write the quadratic, replacing the middle term 11x withe the two numbers we just found: -x+12x
3x^2-x+12x-4 = 0 Factor by grouping:
(3x^2-x)+(12x-4) = 0
x(3x-1)+4(3x-1) = 0
(x+4)(3x-1)=0
x+4=0 or 3x-1 = 0
x= -4 or x= 1/3
The solutions are -4 and 1/3
