Question

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Answer 1

Delta=

$b {}^{2} - 4ac$

Bhaskara=

$- b \frac{ + }{ - } \sqrt{delta} \div 2a$

A) x²+7x=0

a= 1

b= 7

c=0

∆= 7²- 4×1×0

∆= 49-0

√∆= 49

x= -7 +/- 7 ÷ 2

x'= -7+7 = 0

x"= -7-7= -14÷2= -7

S= {-7,0}

B) -3x²+9x=0

a= -3

b= 9

c= 0

∆= 9²-4× (-3)×0

∆= 81-0

√∆= 9

x= -9 +/- 9÷ 2×(-3)

x'= -9+9=0

x"= -9-9= -18÷ (-6) = 3

S={0,3}

C) 2x²+3x=0

a= 2

b= 3

c=0

∆= 3²- 4×2×0

∆=9-0

√∆= 3

x=-3 +/- 3÷ 2×2

x'= -3+3=0

x"= -3-3=-6÷4= -1,5

S={-1,5,0}

D) x²+9x=0

a=1

b= 9

c= 0

∆= 9²-4×1×0

∆=81-0

√∆=9

x= -9 +/- 9÷ 2

x'= -9+9=0

x"= -9-9= -18÷2= -9

S={-9,0}

E) y²-10=0

y²= 10

y= +/- √10

y'= +√10

y"= -√10

F) 2x²+50=0

2(x²+25)

G) -5x²+20=0

-5(x²-4)

-5(x-2)×(x+2)

H) 9x²- 25=0

3²x²-5²

(3x)²-5²

(3x-5)×(3x+5)

I) 5y²-9y-2=0

a= 5

b= -9

c= -2

∆= (-9)²- 4× 5×(-2)

∆= 81+ 40= 121

√∆= 11

y= -(-9) +/- 11÷ 2×5

y'= 9 + 11= 20÷10=2

y"= 9-11= -2÷ 10= -0,2

S={-0,2,2}

J) x²-9x+20=0

a= 1

b= -9

c= 20

∆= -9² -4×1×20

∆= 81- 80=1

√∆= 1

x= -(-9) +/- 1÷ 2

x'= 9+1= 10÷2=5

x"= 9-1= 8÷2= 4

S={4,5}

K) y²+9y+14=0

a= 1

b= 9

c= 14

∆= 9²-4×1×14

∆= 81- 56=25

√∆= 5

y= -9 +/- 5÷ 2

y'= -9+5= -4÷2= -2

y"= -9-5= -14÷2= -7

S= {-7,-2}

L) x²-3x-10=0

a= 1

b= -3

c= -10

∆= -3²-4×1×(-10)

∆= 9+ 40=49

√∆= 7

x= -(-3) +/- 7÷2

x'= 3+7= 10÷2=5

x"= 3-7= -4÷2= -2

S= {-2,5}

M) 2y²+7y+6=0

a= 2

b= 7

c= 6

∆= 7²-4×2×6

∆= 49- 48=1

√∆=1

y= -7 +/- 1÷ 4

y'= -7+1= -6÷4= -1,5

y"= -7-1= -8÷4= -2

S= {-2, -1,5}

N) 4y²-4y+2=0

a= 4

b= -4

c= 2

∆= -4²-4×4×2

∆= 16- 32= -16

√∆= Não existe (É necessário que Delta seja positivo)

O) 5t²-9t+4=0

a= 5

b= -9

c= 4

∆= -9²-4×5×4

∆= 81- 80= 1

√∆= 1

t= -(-9) +/- 1÷ 10

t'= 9+1= 10÷10=1

t"= 9-1= 8÷ 10= 0,8

S={ 0,8,1}