577, 578, 579

ա) x² — 4x + 3

D = b² — 4a * c
D = 16 — 4 * 3 = √28

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 4 + √28 / 2
X₂ = 4 — √28 / 2

2 (x — (4+√28 / 2)) (x — (4-√28 / 2))

բ) x² — 4x + 4

D = b² — 4a * c
D = 16 — 4 * 4 = √32

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 4 + √32 / 2
X₂ = 4 — √32 / 2

2 (x — (4+√32/2)) (x — (4-√32/2))

գ) x² + 4x + 5

D = b² — 4a * c
D = 16 — 4 * 5 = √36 = 6

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 4 + 6 / 2 = 5
X₂ = 4 — 6 / 2 = -1

2 (x — 5) (x + 1)

դ) 3x² — 4x + 1

D = b² — 4a * c
D = 16 + 12 * 1 = √28

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 4 + √28 / 6
X₂ = 4 — √28 / 6

3 (x — (4 + √28 / 6)) (x — (4 — √28 / 6))

ե) 5x² — 6x + 1

D = b² — 4a * c
D = 36 — 20 * 1 = √16 = 4

X₁ = -b + √D / 2a
X₂ = -b — √D / 2a

X₁ = 6 + 4 / 6 = 10/6
X₂ = 6 — 4 / 6 = 2/6

5 (x — 10/6) (x — 2/6)