Resposta:

∆= b² - 4.a.c

x = - b ±√∆/2.a

Explicação passo-a-passo:

a) x² - 10x +25=0

a= 1

b= -10

c= 25

∆= (-10)² - 4.1.25

∆= 100 - 100

∆= 0

x = - (-10) ±√0/2.1

x= +10/2

x= +5

S = { 5}

b) x² -8x -9=0

∆= (-8)² - 4.1.(-9)

∆= 64 + 36

∆= 100

x= - (-8) ±√100/2.1

x= 8 ±10/2

x1= 8+10/2= 18/2=9

x2= 8-10/2= - 2/2 = -1

S = { - 1, 9}

c) x² +5x -150=0

∆= 5² - 4.1.(-150)

∆= 25 + 600

∆= 625

x= - 5 ±√625/2.1

x= - 5 ± 25/2

x1= -5+25/2= 20/2= 10

x2= -5-25/2= - 30/2= -15

S= { -15, 10}

d) 3x² + x -2=0

∆= 1² -4.3.(-2)

∆= 1 + 24

∆= 25

x= - 1 ±√25/2.3

x= -1 ±5/6

x1= -1+5/6= 4/6= 2/3

x2= -1-5/6= -6/6= -1

S = { -1, 2/3}

e) 3x² = 12

x² = 12/3

x²= 4

x= ±√4

x= ±2

S = { -2, 2}