x²-5x+4 = 0
f) x²-x-2 = 0
g) x²-5x-6 = 0
h) x²-x+6 = 0
i) x²-5x+6 = 0
j) x²-x-2 = 0
k) x²+x-2 = 0
l) x²-x-6 = 0
m) x²+5x+4 = 0
n) x²-6x+5 = 0
o) x²-7x+6 = 0
p) x²-2x-8 = 0
q) x²-2x-3 = 0
r) x²-4x+3 = 0

Vamos resolver todas essas equações do segundo grau usando a fórmula de Bhaskara:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

### (a) \( x^2 - 5x + 4 = 0 \)
- \( a = 1 \), \( b = -5 \), \( c = 4 \)
\[
\Delta = (-5)^2 - 4(1)(4) = 25 - 16 = 9
\]
\[
x_1 = \frac{5 + 3}{2} = 4, \quad x_2 = \frac{5 - 3}{2} = 1
\]
Raízes: \( x_1 = 4 \), \( x_2 = 1 \)

### (f) \( x^2 - x - 2 = 0 \)
- \( a = 1 \), \( b = -1 \), \( c = -2 \)
\[
\Delta = (-1)^2 - 4(1)(-2) = 1 + 8 = 9
\]
\[
x_1 = \frac{1 + 3}{2} = 2, \quad x_2 = \frac{1 - 3}{2} = -1
\]
Raízes: \( x_1 = 2 \), \( x_2 = -1 \)

### (g) \( x^2 - 5x - 6 = 0 \)
- \( a = 1 \), \( b = -5 \), \( c = -6 \)
\[
\Delta = (-5)^2 - 4(1)(-6) = 25 + 24 = 49
\]
\[
x_1 = \frac{5 + 7}{2} = 6, \quad x_2 = \frac{5 - 7}{2} = -1
\]
Raízes: \( x_1 = 6 \), \( x_2 = -1 \)

### (h) \( x^2 - x + 6 = 0 \)
- \( a = 1 \), \( b = -1 \), \( c = 6 \)
\[
\Delta = (-1)^2 - 4(1)(6) = 1 - 24 = -23
\]
Raízes: Não há soluções reais (raízes complexas)

### (i) \( x^2 - 5x + 6 = 0 \)
- \( a = 1 \), \( b = -5 \), \( c = 6 \)
\[
\Delta = (-5)^2 - 4(1)(6) = 25 - 24 = 1
\]
\[
x_1 = \frac{5 + 1}{2} = 3, \quad x_2 = \frac{5 - 1}{2} = 2
\]
Raízes: \( x_1 = 3 \), \( x_2 = 2 \)

### (j) \( x^2 - x - 2 = 0 \)
(Similar ao exercício **f**)
Raízes: \( x_1 = 2 \), \( x_2 = -1 \)

### (k) \( x^2 + x - 2 = 0 \)
- \( a = 1 \), \( b = 1 \), \( c = -2 \)
\[
\Delta = (1)^2 - 4(1)(-2) = 1 + 8 = 9
\]
\[
x_1 = \frac{-1 + 3}{2} = 1, \quad x_2 = \frac{-1 - 3}{2} = -2
\]
Raízes: \( x_1 = 1 \), \( x_2 = -2 \)

### (l) \( x^2 - x - 6 = 0 \)
- \( a = 1 \), \( b = -1 \), \( c = -6 \)
\[
\Delta = (-1)^2 - 4(1)(-6) = 1 + 24 = 25
\]
\[
x_1 = \frac{1 + 5}{2} = 3, \quad x_2 = \frac{1 - 5}{2} = -2
\]
Raízes: \( x_1 = 3 \), \( x_2 = -2 \)

### (m) \( x^2 + 5x + 4 = 0 \)
- \( a = 1 \), \( b = 5 \), \( c = 4 \)
\[
\Delta = (

Explore step-by-step solutions to quadratic equations like x²-5x+4, x²-5x-6, and more. This page explains how to apply the quadratic formula and discriminant for real and complex roots. Ideal for students in Grades 7-9.

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