Question

1) Identifique as raízes de cada equação :  a) x² - 5x + 6 = 0 b) 2x² -10x + 8 = 0 c) -x² + 7x - 14 = 0 d)  x² - 7x + 6 = 0​

Answer 1

Explicação passo-a-passo:

a) x² - 5x + 6 = 0

$x = \frac{ - ( -5)± \sqrt{( - 5)^{2} - 4 \times 1 \times 6 } }{2 \times 1}$

$x = \frac{5± \sqrt{25 - 24} }{2} = \frac{5± \sqrt{1} }{2}$

$x = \frac{5 + 1}{2} = \frac{6}{2} = 3$

$x = \frac{5 - 1}{2} = \frac{4}{2} = 2$

b) 2x² -10x + 8 = 0

$x = \frac{ -( - 10)± \sqrt{( - 10) {}^{2} - 4 \times 2 \times 8 } }{2 \times 2}$

$x = \frac{10± \sqrt{100 - 64} }{4} = \frac{10± \sqrt{36} }{4}$

$x = \frac{10 + 6}{4} = \frac{16}{4} = 4$

$x = \frac{10 - 6}{4} = \frac{4}{4} = 1$

c) -x² + 7x - 14 = 0

$x = \frac{ - 7± \sqrt{7 {}^{2} - 4 \times ( - 1) \times ( - 14)} }{2 \times ( - 1)}$

$x = \frac{ - 7± \sqrt{49 - 56} }{ (- 2)}$

$x = \frac{ - 7± \sqrt{ - 7} }{ - 2}$

d)  x² - 7x + 6 = 0

$x = \frac{ - ( - 7)± \sqrt{( - 7)^{2} - 4 \times 1 \times 6} }{2 \times 1}$

$x = \frac{7± \sqrt{49 - 24} }{2} = \frac{7± \sqrt{25} }{2}$

$x = \frac{7 + 5}{2} = \frac{12}{2} = 6$

$x = \frac{7 - 5}{2} = \frac{2}{2} = 1$