Bonjour,
Question 1 :
u = x² + 3 v = x + 1
u' = 2x v' = 1
[tex]f'(x)=\frac{u'v-uv'}{v^2} = \frac{2x \times (x+1) -(x^2+3)\times1}{(x+1)^2} = \frac{2x^2 +2x -x^2 -3}{(x+1)^2} = \frac{x^2 + 2x - 3}{(x+1)^2}[/tex]
Question 2 :
On reconnaît un trinôme du second degré :
P(x) = x² + 2x - 3
Δ = b² - 4ac = 2² - 4 x 1 x (-3) = 4 + 12 = 16
[tex]x_1 = \frac{-2-\sqrt{16} }{2} = -3\\x_2 = \frac{-2+\sqrt{16} }{2} = 1[/tex]
a(x - x₁)(x-x₂) = 1(x - (-3))(x-1) = (x + 3)(x - 1)
