Question

1) Resolva em IR.

A)
$2 {m}^{2} - m - 6 = 0$
B)
$(x + 4)(x - 1) = 5x + 20$

Answer 1

A)
 2m² - m - 6 =0

a=2
b=-1
c=-6

Δ=b² -4ac
Δ=(-1)² - 4 (2)(-6)
Δ=1+48
Δ=49

$m= \frac{-b\pm \sqrt{\Delta} }{2a} =~~ \frac{-(-1)\pm \sqrt{49} }{2.(2)} =~~ \frac{1\pm7}{4} \\ \\ m'= \frac{1+7}{4} = \frac{8}{4} =2 \\ \\ m"= \frac{1-7}{4} =- \frac{6}{4} =- \frac{3}{2} \\ \\ S=\{- \frac{3}{2} ,2\}$ 


B)
x² + 3x - 4 = 5x + 20
x² + 3x - 5x - 4 - 20 =0

x² - 2x - 24 = 0

a=1
b=-2
c=-24

Δ=b²-4ac
Δ=(-2)²-4(1)(-24)
Δ=4+96
Δ=100

$x= \frac{-b\pm \sqrt{\Delta} }{2a} = \frac{-(-2)\pm \sqrt{100} }{2} =~~ \frac{2\pm10}{2} \\ \\ x'= \frac{2+10}{2} = \frac{12}{2} =6 \\ \\ x"= \frac{2-10}{2} =- \frac{8}{2} =-4 \\ \\ S=\{-4,6\}$

Answer 2

Olá!!

Resolução!!!

a)

2m² - m - 6 = 0

a = 2, b = - 1, c = - 6

∆ = b² - 4ac
∆ = ( - 1 )² - 4 • 2 • ( - 6 )
∆ = 1 + 48
∆ = 49

m = - b ± √∆ / 2a
m = - ( - 1 ) ± √49 / 2 • 2
m = 1 ± 7 / 4
m' = 1 + 7 / 4 = 8/4 = 2
m" = 1 - 7 / 4 = - 6/4 : 2 = - 3/2

S = { - 3/2, 2 }

b)

( x + 4 ) ( x - 1 ) = 5x + 20
x² - x + 4x - 4 = 5x + 20
x² - x + 4x - 4 - 5x - 20 = 0
x² - x + 4x - 5x - 20 - 4 = 0
x² - 2x - 24 = 0

a = 1, b = - 2, c = - 24

∆ = b² - 4ac
∆ = ( - 2 )² - 4 • 1 • ( - 24 )
∆ = 4 + 96
∆ = 100

x = - b ± √∆ / 2a
x = - ( - 2 ) ± √100 / 2 • 1
x = 2 ± 10 / 2
x' = 2 + 10 / 2 = 12/2 = 6
x" = 2 - 10 / 2 = - 8/2 = - 4

S = { - 4, 6 }

Espero ter ajudado!!!