Respuesta :
Answer:
see explanation
Step-by-step explanation:
Solve the equation
x² + 3x - 4 = 0 ← in standard form
(x + 4)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 1 = 0 ⇒ x = 1
The zeros are x = - 4 and x = 1
These split the domain into 3 intervals, that is
( - ∞ , - 4), (- 4, 1), (1 , +∞)
Choose a rest point in each interval, substitute into the quadratic and check the sign.
x = - 5 : (- 5 + 4)(- 5 - 1) = (- 1)(- 6) = + 6 > 0
x = 0 : (0 + 4)(0 - 1) = (4)(- 1) = - 4 < 0
x = 5 : (5 + 4)(5 - 1) = (9)(4) = 36 > 0
Hence x² + 3x - 4 > 0 has solution
(- ∞, - 4) ∪ (1, + ∞ )
