Răspuns:
Explicație pas cu pas:
C) x² - 4x + 5 < 0
x² - 4x + 5 = 0 ; a = 1 ; b = -4 ; c = 5 ;
Δ = b²-4ac = (-4)²-4·1·5 = 16-20 = -4 < 0 =>
=> x²-4x+5 > 0 ; (∀) x ∈ R =>
solutia inecuatiei = {∅}
E) - x² - x - 1 ≥ 0
- x² - x - 1 = 0 ; a = -1 ; b = -1 ; c = -1 ;
Δ = b²-4ac = (-1)²-4(-1)(-1) = 1-4 = -3 < 0 =>
- x² - x - 1 < 0 ; (∀) x ∈ R =>
solutia inecuatiei = {∅}
F) 2x² + 7x +3 < 0
2x² + 7x +3 = 0 ; a = 2 ; b = 7 ; c = 3 ;
Δ = b²-4ac = 7²-4·2·3 = 49-24 = 25 => √Δ = √25 = 5
x₁,₂ = (-b±√Δ)/2a = (-7±5)/4
x₁ = (-7-5)/4 = -12/4 = -3
x₂ = (-7+5)/4 = -2/4 = -1/2
x I -∞ -3 -1/2 +∞
2x² + 7x +3 I ++++++++0----0+++++++
=> solutia inecuatiei = x ∈ (-3 ; -1/2)
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