Question

1) Determine as raizes  das equações :

A) x² + x - 6 = 0

B) x² +4x - 5= 0

C) 2x² - 9x + 4 = 0

D) x² - 10x + 24 =0

Answer 1

a) $x^{2} + x - 6 = 0$
Δ = 1 - 4.1.(-6)
Δ = 1 + 24  Δ = 25

x = $\frac{-1 +-5}{2}$
x1 = $\frac{4}{2}$ = 2
x2 = $\frac{-6}{2}$ = -3

S= {2, -3}

b) $x^{2} + 4x - 5 = 0$
Δ = 16 - 4.1.(-5)
Δ = 16 + 20  Δ= 36

x = $\frac{-4 +-6}{2}$
x1 = $\frac{2}{2}$ = 1
x2 = $\frac{-10}{2}$ = -5

S = {1,5}

c) $2x^{2} - 9x + 4 = 0$
Δ = 81 - 4.2.4
Δ = 81 - 32  Δ = 49

x = $\frac{9 +- 7}{2}$
x1 = $\frac{16}{4}$ = 4
x2 = $\frac{2}{4}$ = $\frac{1}{2}$

S = {4,$\frac{1}{2}$}

d) $x^{2} - 10x + 24 = 0$
Δ = 100 - 4.1.24
Δ = 100 - 96  Δ = 4

x = $\frac{10 +- 2}{2}$
x1 = $\frac{12}{2}$ = 6
x2 = $\frac{8}{2}$ = 4

S = {6,4}