Question

determinar as raizes de:
y= -x²+2x+3
f(x)=x²-2x+1
f(x)=-x2+x-1

Answer 1

Y= -$x^{2}$ + 2x + 3

Δ= b² - 4 × a × c

Δ= (-2)² -  4 × (-1) × 3

Δ= 4 + 12

Δ= 16

x= -b ± √Δ ÷ 2 x a

x= -2 ± √16 ÷ 2 × (-1)

x= -2 ± 4 ÷ -2

$x_{1}$= -2 + 4 ÷ -2

$x_{1}$= 2 ÷ -2

$x_{1}$= -1

$x_{2}$= -2 -4 ÷ -2

$x_{2}$= -6 ÷ -2

$x_{2}$= +3

Raízes (-1) e (3)

f(x)=$x^{2}$-2x+1

Δ= b² - 4 × a × c

Δ= (-2)² -  4 × 1 × 1

Δ= 4 - 4

Δ= 0

x= -b ± √Δ ÷ 2 x a

x= - (-2) ± √0 ÷ 2 × 1

x= 2 ± 0 ÷ 2

$x_{1}$= 2 + 0 ÷ 2

$x_{1}$= 2 ÷ 2

$x_{1}$= 1

$x_{2}$= 2 + 0 ÷ 2

$x_{2}$= 2 ÷ 2

$x_{2}$= 1

Raízes (1) e (1)

As raízes são iguais por que o valor de Δ é 0

f(x)=$x^{2}$+x-1

Δ= b² - 4 × a × c

Δ= 1² -  4 × 1 × (-1)

Δ= 1 + 4

Δ= 5

x= -b ± √Δ ÷ 2 x a

x= -1 ± √5 ÷ 2 × 1

x= -1 ± 2,23 ÷ 2

$x_{1}$= -1 + 2,23 ÷ 2

$x_{1}$= 3,23 ÷ 2

$x_{1}$= 0,615

$x_{2}$= -1 - 2,23 ÷ 2

$x_{2}$= -3,23 ÷ 2

$x_{2}$= -1,615

Raízes (0,615) e (-1,615)

Espero ter ajudado :)