Matematyka Matura Podstawowa Maj 2015 Zadanie 26

Rozwiąż nierówność 2x^2 - 4x > (x+3)(x-2)
2x^2 - 4x > x^2 - 2x + 3x - 6
2x^2 - 4x > x^2 + x - 6
2x^2 - 4x - x^2 - x +6 > 0
x^2 - 5 x + 6 > 0
a = 1 , b = -5, c = 6
\Delta = b^2 - 4ac
\Delta = (-5)^2 - 4*1*6 = 25 - 24 = 1
\sqrt{\Delta} = 1
x_1 = \frac{-b+\sqrt{\Delta}}{2a}
x_1 = \frac{5+1}{2} = \frac{6}{2} = 2
x_2 = \frac{-b-\sqrt{\Delta}}{2a}
x_2 = \frac{5-1}{2} = \frac{4}{2} = 3
(x-2)(x-3) > 0