Question

1)Ache as raízes das equações:
a) x² – x – 20 = 0
b) x² – 3x -4 = 0
c) x² – 8x + 7 = 0
preciso para amanhã, por favor!

Answer 1

a)

$x^{2}$ - x - 20 = 0

-b ± $\frac{\sqrt{b^{2} - 4 . a . c } }{2 . a}$

a = 1

b = -1

c = - 20

1 ± $\frac{(-1)^{2} - 4 . 1 . ( - 20 ) }{2 . 1}$

1 ± $\frac{\sqrt{1 + 80 } }{2}$

1 ± $\frac{\sqrt{81} }{2}$

1 ± $\frac{9}{2}$

x' = $\frac{1 + 9 }{2}$

x' = $\frac{10}{2}$

x' = 5

x'' = $\frac{1 - 9}{2}$

x'' = - $\frac{8}{2}$

x'' = - 4

b)

$x^{2}$ - 3x - 4= 0

- b ± $\frac{\sqrt{b^{2} - 4 . a . c } }{2 . a}$

a = 1

b = - 3

c = 4

3 ± $\frac{\sqrt{(-3)^{2} - 4 . 1 . ( -4 ) } }{2.1}$

3 ± $\frac{\sqrt{9 + 16 } }{2}$

3 ± $\frac{\sqrt{25} }{2}$

3 ± $\frac{5}{2}$

x' = $\frac{3 + 5}{2}$

x' = $\frac{8}{2}$

x' = 4

x'' = $\frac{3 - 5}{2}$

x'' = - $\frac{2}{2}$

x'' = - 1

c)

$x^{2}$ - 8x + 7 = 0

- b ± $\frac{\sqrt{b^{2} - 4 . a . c } }{2 . a}$

a = 1

b = - 8

c = 7

8 ± $\frac{\sqrt{(-8)^{2} - 4 . 1 . 7 } }{2.1}$

8 ± $\frac{\sqrt{64 - 28 } }{2}$

8 ± $\frac{\sqrt{36} }{2}$

8 ± $\frac{6}{2}$

x' = $\frac{8 + 6}{2}$

x' = $\frac{14}{2}$

x' =7

x'' = $\frac{8 - 6}{2}$

x'' = $\frac{2}{2}$

x'' = 1