Question

Rozwiąż .

Answer 1

1.

-2x^2 + 3x + 5 = 0

a = -2,  b = 3,   c = 5

D(delta) = b^2 - 4ac = 3^2 -4*(-2)*5 = 49

VD = 7

x1 = (-b-VD)/2a = (-3-7)/(-4) = -10/(-4) = 2,5

x2 = (-b+VD)/2a = (-3+7)/(-4) = -1

 

2.

5x^2 + 2x = 3

5x^2 +2x -3 = 0

D =4 + 60 = 64

VD = 8

x1 = (-2-8)/10 -1

x2 = (-2+8)/10 = 0,6

 

3.

2x^2 + 5x -3 < 0

przyrównujemy do zera;

2x^2 + 5x -3 < 0

D = 25 + 24 = 49

VD = 7

x1 = (-5-7)/4 = -12/4 = -3

x2 = (-5+7)/4 = 2/4 = 0,5

 

a = 2 > 0, ramiona paraboli skierowane w górę

x e (-3; 0,5)

 

4.

6x^2 <= x+2

6x^2 - x - 2 <= 0

D = 1 + 48 = 49

VD = 7

x1 = (1-7)/12 = -6/12 = -1/2

x2 = (1+7)/12 = 8/12 = 2/3

 

a = 6 > 0, ramiona paraboli są skierowane w górę

x e < -1/2; 2/3 >