ax^{2} + bx + c = a(x  x_{1})(x  x_{2})
x_{1} and x_{2} are roots ob quadratic equation ax^{2} + bx + c = 0
D = √(b^{2}  4ac)
x_{12} = ( b ± √D) / 2a
If D > 0, quadratic equation has 2 real roots.
If D = 0, ...... has 1 real root.
If D < 0, ..... does not have real roots and can not be factorized.
~~~~~~~~~~~~
4x^{2} + 27x  7 = 0
D = 27^{2} + 112 = 841 = 29^{2}
x_{1} = ( 27  29) / 8 =  7
x_{2} = ( 27 + 29) / 8 = 1/4
4x^{2} + 27x  7 = 4(x  1/4)(x + 7) = (4x  1)(x + 7)
11/25/2013

Nataliya D.