Question

10) Encontre as raízes das equações:
a) x² - x - 20=0

b) x²-3x - 4=0

C) x² - 8x + 7=0​

Answer 1

Resposta:

a) raízes (-4,5)   b) raízes (-1,4)  c) Raízes (1,7)

Explicação passo-a-passo:

a) x² - x - 20=0  =>Δ= b²-4ac =>Δ= (-1)² - 4 (1) (-20) => Δ= 1 + 80 =>  Δ= 81

x = -b ±√Δ/2a =>  x = 1 ± 9/2 => $x_{1} = \frac{1+9}{2} = \frac{10}{2} = 5\\x_{2} = \frac{1-9}{2} = \frac{-8}{2} = -4$

b) x²-3x - 4=0  Δ= b²-4ac =>Δ= (-3)² - 4 (1) (-4) => Δ= 9 + 16 =>  Δ= 25

x = -b ±√Δ/2a =>  x = 3 ± 5/2 => $x_{1} = \frac{3+5}{2} = \frac{8}{2} = 4\\x_{2} = \frac{3-5}{2} = \frac{-2}{2} = -1$

C) x² - 8x + 7=0​ Δ= b²-4ac =>Δ= (-8)² - 4 (1) (7) => Δ= 64 - 28 =>  Δ= 36

x = -b ±√Δ/2a =>  x = 8 ± 6/2 => $x_{1} = \frac{8+6}{2} = \frac{14}{2} = 7\\x_{2} = \frac{8-6}{2} = \frac{2}{2} = 1$