Resuelve las siguientes ecuaciones de segundo grado:
a) 4x2 -16= 0
b) 3x2 + 6x = 0
c) 2x 2-7x- 4= 0
Respuestas a la pregunta
Respuesta:
a) 4x² -16= 0
ax² + bx + c = 0
a = 4
b = 0
c = -16
Aplicamos la formula general
-b+-√b² - 4ac - (0)+-√(0)² - 4 · (4) · (-16) 0+-√0 + 256 0+-16
x = -------------------- = ----------------------------------- = ------------------- = ----------
2a 2 · (4) 8 8
0 + 16 16 0 - 16 -16
= ----------- = ------- = 2 --------- = -------- = -2
8 8 8 8
x = 2
x = -2
b) 3x² + 6x = 0
ax² + bx + c = 0
a = 3
b = 6
c = 0
Aplicamos la formula de ecuaciones de segundo grado
-b+-√b² - 4ac - (6)+-√(6)² - 4 · (3) · (0) -6+-√36 - 0 -6+-6
x = ------------------ = --------------------------------- = ------------------ = ---------
2a 2 · (3) 6 6
-6+6 0 -6-6 -12
= -------- = -------- = 0 --------- = -------- = -2
6 6 6 6
x = 0
x = -2
c)2x² - 7x - 4 = 0
ax² + bx + c = 0
a = 2
b = -7
c = -4
Aplicamos la formula
-b+-√b²-4ac - (-7)+-√(-7)²-4 · (2) · (-4) +7+-√49 + 32 7+-√81
x = -------------------- = ----------------------------------- = --------------------- = ---------------
2a 2 · (2) 4 4
7+-9 7 + 9 16 7 - 9 -2
= ------------ = --------- = -------- = 4 -------- = -------- = -1/2
4 4 4 4 4
x = 4
x = -1/2