Question

quantas sao as soluçoes inteiras da inequaçao -x2 + 13x - 40 > 0

Answer 1

-x²+13x-40 > 0

-x²+13x-40 = 0
(-x + 8) (x-5) = 0
x = 8  e  x = 5

_____ 5_____8_____

x < 5, x= 0 --> -0²+13(0)-40 = -40 (negative)

5 <  x < 8, x= 6 --> -6²+13(6)-40 = -36+78-40 = 2 (Positive)

x > 8, x = 9 --> -9²+13(9)-40 = -81+117-40 = -3 (Negative)

----- 5 ++++ 8 -----

f(x) > 0, took Poistive

S = { 5  < x  < 8 }