Question

a)x²+x-2=0

b) x²-5x+6=0

c) x² -4x -4=0​

Answer 1

a)x²+x-2=0

a=1

b=1

c=-2

∆=b²-4.a.c

∆=(1)²-4.(1).(-2)

∆=1+8

∆=9

x'=-1+√9/2=-1+3/2=2/2=1

x"=-1-√9/2=-1-3/2=-4/2=-2

S={ -2,1}

b) x²-5x+6=0

a=1

b=-5

c=+6

∆=b²-4.a.c

∆=(-5)²-4.(1).(6)

∆=25-24

∆=1

x'=-(-5)+√1/2

x'=5+1/2

x'=6/2

x'=3

x"=-(-5)-√1/2

x"=5-1/2

x"=4/2

x"=2

S={2,3}

c) x² -4x -4=0

a=1

b=-4

c=-4

∆=b²-4.a.c

∆=(-4)²-4.(1).(-4)

∆=16+16

∆=32

x'=-(-4)+√32/2

x'=(4+4√2)/2

x'=(2+2√2)

x"=-(-4)-√32/2

x"=(4-4√2)/2

x"=(2-2√2)

S={ 2+√2; 2-√2}

Espero ter ajudado!

Answer 2

a) a=1 b=1 c=-2

∆=b²-4ac

∆=1²-4.1.(-2)

∆=1+8

∆=9

x=-b±√∆/2a

x=-1±√9/2

x=-1±3/2

x,=-1+3/2

x,=2/2

x,=1

x,,=-1-3/2

x,,=-4/2

x,,=-2

b) a=1 b=-5 c=6

∆=b²-4ac

∆=(-5)²-4.1.6

∆=25-24

∆=1

x=-b±√∆/2a

x=-(-5)±√1/2

x=5±1/2

x,=5+1/2

x,=6/2

x,=3

x,,=5-1/2

x,,=4/2

x,,=2

c) a=1 b=-4 c=-4

∆=b²-4ac

∆=(-4)²-4.1.(-4)

∆=16+16

∆=32

∆=∅