Question

Dada a função f(x) =
x^2 + 2x + 1, determine:

f(x) = 0

Answer 1

$f(x) = x^{2} + 2x + 1$

Por Bháskara
$x = \frac{-b \pm \sqrt{b^{2} - 4 \cdot a \cdot c}}{2 \cdot a} \\\\ x = \frac{-2 \pm \sqrt{2^{2} - 4 \cdot 1 \cdot 1}}{2 \cdot 1} \\\\ x = \frac{-2 \pm \sqrt{4 - 4}}{2} \\\\ x = \frac{-2}{2} = \boxed{-1}$

Por Soma e Produto
$\_ + \_ = \frac{-b}{a}\\\\ \_ \cdot \_ = \frac{c}{a}$
_ + _ = -2
_ · _ = 1

(-1) + (-1) = -2
(-1) · (-1) = 1

Por Derivadas
$f(x) = x^{2} + 2x + 1 \Rightarrow f'(x) = 2x + 2$
$2x + 2 = 0 \\ 2x = -2 \\\\ x = \frac{-2}{2} = \boxed{-1}$

Resposta: f(-1) = 0