Question

Resuelve las siguientes desigualdades cuadráticas:
a) x² < 3 – 2x
b) x² ≥ 5 – x + 1
c) 2x²-9x +3 ≤ -1
d) x²– 5x + 6 > 0

Answer 1

a) x² < 3 – 2x
x² - 3 + 2x < 0
x² + 2x - 3 < 0
(x + 3 ) (x -1 ) < 0. (x = -3) ; (x = 1)

b) x² ≥ 5 – x + 1
x² ≥ 6 – x
x² + x - 6 ≥ 0
a b. c
formula general:
x =( b +/- raiz (b^2 - 4ac))/2a
x = (- 1 raiz (1 + 24)/ 2
x = (- 1 raiz (25) )/ 2
x = (-1 (+/-) 5)/ 2. ( x = 4/2 ); ( x = 6/2
(x = 2) ; (x = 3)

c) 2x²-9x +3 ≤ -1
2x²-9x +3 + 1 ≤ 0
2x²-9x + 4 ≤ 0
(2x - 8) (2x - 1) (x = 8/2) ; (x = 1/2)
(x = 4) ; ( x = 1/2)

d) x²– 5x + 6 > 0
(x - 3 ) (x - 2 ) > 0
(x = 3) ; (x = 2)
Espero que te ayude estás respuestas