SOLUTION: factor the quadratic expression completely, and find the roots of the expression. 12x^2 +7x-12

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: factor the quadratic expression completely, and find the roots of the expression. 12x^2 +7x-12      Log On


   

Question 600406: factor the quadratic expression completely, and find the roots of the expression.
12x^2 +7x-12
Answer by w_parminder(53) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E2%2B7x-12
Using the method of splitting the middle term, it can be written as
12x%5E2%2B16x-9x-12
OR
%28+12x%5E2%2B16x+%29-%28+9x%2B12+%29 (taking out -ve sign common from the last two terms)
OR
4x%28+3x%2B4+%29-3%28+3x%2B4+%29 (Taking out '4x' common from first two & '3' from last two terms)
Now (3x+4) is common in both terms, so the above expression can be written as
( 3x+4 )( 4x-3 )
these are the factors of the given expression
we can now find its roots by equating the factors with ZERO
i.e. 3x + 4 = 0
which gives x = -4/3
& 4x - 3 = 0
which gives x = 3/4
So the roots are -4/3 & 3/4