Question

6) Determine As Raizes Das Funçoes
A) Y=x2-7x+10 (x2 o 2 ta elevado no x)
B) Y=x2+2x+1 (x2 o 2 tbm ta elevado no x)
C) Y=2x2-3x+4 (2x2 2 ta elevado no x)

Answer 1

Raízes

A) y = x² - 7x + 10
Δ = b² - 4 × a × c 
Δ = -(-7)² - 4 × (1) + (10)
Δ = 49 - 40
Δ = 9

x1 = -b + √Δ ÷ 2 × a
x1 = -(-7) + √9 ÷ 2 × 1
x1 = 7 + 3 ÷ 2
x1 = 10 ÷ 2
x1 = 5

x2 = -b - √Δ ÷ 2 × a
x2 = -(-7) - √9 ÷ 2 × 1
x2 = 7 - 3 ÷ 2 
x2 = 4 ÷ 2
x2 = 2

B) y = x² + 2x + 1
Δ = b² - 4 × a × c
Δ = (2)² - 4 × (1) × 1
Δ = 4 - 4
Δ = 0

x1 = -b + √Δ ÷ 2 × a
x1 = -(2) + √0 ÷ 2 × 1
x1 = -2 + 0 ÷ 2
x1 = -2 ÷ 2
x1 = -1

x2 = -b - √Δ ÷ 2 × a
x2 = -(2) - √0 ÷ 2 × 1
x2 = -2 - 0 ÷ 2
x2 = -2 ÷ 2
x2 = -1

C) y = 2x² - 3x + 4
Δ = b² - 4 × a × c
Δ = (-3)² - 4 × 2 × 4
Δ = 9 - 32
Δ = -23

Para Δ < 0 não há raiz.