Question

1°) Encontre as raízes das equações abaixo:

a) x² - 5x + 6 = 0
b) -x² + 2x - 1 = 0
c) x² - 7x - 18 = 0
d) x² - 2x - 3 = 0
e) 3x² - 15x = 0​

Answer 1

a) x² - 5x + 6 = 0
∆=b²-4ac
∆=(-5)²-4•1•6
∆=25-24→∆=1

x=-b±√∆/2a
x=-(-5)±√1/2•1
x=5±1/2
x’=5+1/2→x’=6/2→x’=3
x”=5-1/2→x”=4/2→x”=2

x={2;3}

b) -x² + 2x - 1 = 0
∆=b²-4ac
∆=2²-4•(-1)•(-1)
∆=4-4
∆=0

x=-b±√∆/2a
x=-2±√0/2(-1)
x=-2±0/-2
x=-2/-2
x=1
*Obs.: quando ∆=1, x’ e x” são iguais.

x={1}

c) x² - 7x - 18 = 0
∆=b²-4ac
∆=(-7)²-4•1•(-18)
∆=49+72→∆=121

x=-b±√∆/2a
x=-(-7)±√121/2•1
x=7±11/2
x’=7+11/2→x’=18/2→x’=9
x”=7-11/2→x”=-4/2→x”=-2

x={-2;9}

d) x² - 2x - 3 = 0
∆=b²-4ac
∆=(-2)²-4•1•(-3)
∆=4+12→∆=16

x=-b±√∆/2a
x=-(-2)±√16/2•1
x=2±4/2
x’=2+4/2→x’=6/2→x’=3
x”=2-4/2→x”=-2/2→x”=-1

x={-1;3}

e) 3x² - 15x = 0​
3x(x-5)=0
3x=0
x=0/3→x’=0

(x-5)=0
x-5=0
x”=5

x={0;5}

Espero ter ajudado!
=)