Question

3) Resolva as equações: a) 2x²−5x−3=0 b)–2x² +3x+5=0 c) x²−4x+4=0 d) x²+3√2x+4,5=0 e) 4x−x(x−4)=−9 ​

Answer 1

Resposta:

Explicação passo-a-passo:

a) 2x²-5x-3=0

Aplique a fórmula de Bhaskara

a= 2  b= -5  c= -3

Δ= b²- 4 × a × c

Δ= (-5)² - 4 × 2 × (-3)

Δ= 25 + 24

Δ= 49

x= -b ± √Δ / 2 × a

x= -(-5) ± $\sqrt{49}$ / 2 × 2

x= 5 ± 7 / 4

x1= 5 - 7 / 4

x1= -2 / 4

x2= 5 + 7 / 4

x2= 12/4

x2= 3

S= {-2/4 , 3}

b) -2x²+3x+5=0

a= -2  b= 3  c= 5

Δ= b²- 4 × a × c

Δ= 3² - 4 × (-2) × 5

Δ= 9 + 40

Δ= 49

x= -b ± √Δ / 2 × a

x= -3 ± $\sqrt{49}$ / -4

x= -3 ± 7 / -4

x1= -3 - 7 / -4

x1= -10/-4

x1= 2,5

x2= -3+7/-4

x2= 4/-4

x2= 1

S= {2,5 , 1}

c) x²-4x+4=0

a= 1  b= -4  c=4

Δ= b²- 4 × a × c

Δ= (-4)² -4 × 1 × 4

Δ= 16 - 16

Δ= 0

x= -b ± √Δ / 2 × a

x= -(-4) ± $\sqrt{0}$ / 2 × 1

x= 4 / 2

x= 2

S= {2}