Question

6)resolva as equaçoes do 2° grau em R. A)x²+5x+6=0 b)x²+7x+12=0 c)x²+5x+4=0 d)2x²+3x+1=0 e)x2-18x+45=0 f)-x²-x+30=0 g)x²-6x+99=0 h)x²-3x+10=0 i)5x²+6x+3=0 j)7x²+x+2=0 k)2x²5x-3=0 l)6x²+x-1=0 m)6x²-13x+6=0 n)5x²-11x+2=0 o)x²-2x+1=0 p)x²-4x+5=0 q)4x³+11x-3=0

Mim ajude pfvvvv

Answer 1

Resposta:

ITEM A

x² + 5x + 6 = 0

a = 1 ; b = 5 ; c = 6

∆ = b² – 4ac

∆ = 5² – 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

ITEM B

x² + 7x + 12 = 0

a = 1 ; b = 7 ; c = 12

∆ = b² – 4ac

∆ = 7² – 4 × 1 × 12

∆ = 49 – 48

∆ = 1

x = – b ± √∆ / 2a

x = – 7 ± √1 / 2 × 1

x = – 7 ± 1 / 2

x' = – 7 – 1 / 2 → x' = – 8 / 2 → x' = – 4

x" = – 7 + 1 / 2 → x" = – 6 / 2 → x" = – 3

ITEM C

x² + 5x + 4 = 0

a = 1 ; b = 5 ; c = 4

∆ = b² – 4ac

∆ = 5² – 4 × 1 × 4

∆ = 25 – 16

∆ = 9

x = – b ± √∆ / 2a

x = – 5 ± √9 / 2 × 1

x = – 5 ± 3 / 2

x' = – 5 – 3 / 2 → x' = – 8 / 2 → x' = – 4

x" = – 5 + 3 / 2 → x" = – 2 / 2 → x" = – 1

ITEM D

2x² + 3x + 1 = 0

a = 2 ; b = 3 ; c = 1

∆ = b² – 4ac

∆ = 3² – 4 × 2 × 1

∆ = 9 – 8

∆ = 1

x = – b ± √∆ / 2a

x = – 3 ± √1 / 2 × 2

x = – 3 ± 1 / 4

x' = – 3 – 1 / 4 → x' = – 4 / 4 → x' = – 1

x" = – 3 + 1 / 4 → x" = – 2 / 4 → x" = – 0,5

ITEM E

x² – 18x + 45 = 0

a = 1 ; b = – 18 ; c = 45

∆ = b² – 4ac

∆ = ( – 18 )² – 4 × 1 × 45

∆ = 324 – 180

∆ = 144

x = – b ± √∆ / 2a

x = 18 ± √144 / 2 × 1

x = 18 ± 12 / 2

x' = 18 – 12 / 2 → x' = 6 / 2 → x' = 3

x" = 18 + 12 / 2 → x" = 30 / 2 → x" = 15

ITEM F

– x² – x + 30 = 0

a = – 1 ; b = – 1 ; c = 30

∆ = b² – 4ac

∆ = ( – 1 )² – 4 × ( – 1 ) × 30

∆ = 1 + 120

∆ = 121

x = – b ± √∆ / 2a

x = 1 ± √121 / 2 × ( – 1 )

x = 1 ± 11 / – 2

x' = 1 – 11 / – 2 → x' = – 10 / – 2 → x' = 5

x" = 1 + 11 / – 2 → x" = 12 / – 2 → x" = – 6