Question

Determine os zeros (raízes) das seguintes funções: a) f(x) = x 2 – 3x + 2 b) f(x) = -2x 2 – 5x c) f(x) = -3x 2 + 6 d) f(x) = - x² - 6x – 9

Answer 1

Oie, Td Bom?!

a)

$f(x) = x {}^{2} - 3x + 2 \\ 0 = x {}^{2} - 3x + 2 \\ x {}^{2} - 3x + 2 = 0 \\ x {}^{2} - x - 2x + 2 = 0 \\ x \: . \: (x - 1) - 2(x - 1) = 0 \\ (x - 1) \: . \: (x - 2) = 0$

$x - 1 = 0⟶ x= 1 \\ x - 2 = 0⟶x = 2$

S = $\left \{ x_{1} = 1 \: , \: x_{2} = 2 \right \}$

b)

$f(x) = - 2x {}^{2} - 5x \\ 0 = - 2x {}^{2} - 5x \\ - 2x {}^{2} - 5x = 0 \\ - x \: . \: (2x + 5) = 0 \\ x \: . \: (2x + 5) = 0$

$x = 0\\ 2x + 5 = 0⟶x = - \frac{5}{2}$

S = $\left \{ x_{1} = - \frac{5}{2} \: , \: x_{2} = 0 \right \}$

c)

$f(x) = - 3x {}^{2} + 6 \\ 0 = - 3x {}^{2} + 6 \\ 3x {}^{2} = 6 \\ x {}^{2} = 2 \\ x = ± \sqrt{2}$

$x = - \sqrt{2} \\ x = \sqrt{2}$

S = $\left \{ x_{1} = - \sqrt{2} \: , \: x_{2} = \sqrt{2} \right \}$

d)

$f(x) = - x {}^{2} - 6x - 9 \\ 0 = - x {}^{2} - 6x - 9 \\ 0 + x {}^{2} + 6x + 9 = 0 \\ x {}^{2} + 6x + 9 = 0 \\ (x + 3) {}^{2} = 0$

$x + 3 = 0⟶x = - 3$

S = $\left \{ - 3\right \}$

Att. Makaveli1996