Jawab:
(a.)  3x² - 45x + 163 = 0
(b.)  3x² + 21x + 31 = 0
(c.)  48x² + 12x - 5 = 0
(d.)  3x² - 12x - 11 = 0

Penjelasan:
Diketahui persamaan
3x² + 3x - 5 = 0
Ax² + Bx + C = 0
A = 3, B = 3, C = -5

Akar-akarnya α dan β

Teori Vieta
α + β = -B/A, maka
α + β = -3/3
-->  α + β = -1

αβ = C/A, maka
-->  αβ = -5/3

TENTUKAN
Pers. kuadrat yg akarnya

(a.)  α+8 dan β+8
(α+8) + (β+8) = -B/A
α + β + 16 = -B/A
-1 + 16 = -B/A
-B/A = 15
(α+8)(β+8) = C/A
αβ + 8α + 8β + 64 = C/A
αβ + 8(α + β) + 64 = C/A
(-5/3) + 8(-1) + 64 = C/A
(-5/3) - 8 + 64 = C/A
(-5/3) + 56 = C/A
(-5/3) + (168/3) = C/A
C/A = 163/3
-B/A = 15  dan  C/A = 163/3
-B/A = -45/-3      C/A = -163/-3
A = -3, B = 45, C = -163
Ax² + Bx + C = 0  maka pers.
-3x² + 45x - 163 = 0  atau
3x² - 45x + 163 = 0

(b.)  α-3 dan β-3
(α-3) + (β-3) = -B/A
α + β - 6 = -B/A
-1 - 6 = -B/A
-B/A = -7
(α-3)(β-3) = C/A
αβ - 3α - 3β + 9 = C/A
αβ - 3(α + β) + 9 = C/A
(-5/3) - 3(-1) + 9 = C/A
(-5/3) + 3 + 9 = C/A
(-5/3) + 12 = C/A
(-5/3) + (36/3) = C/A
C/A = 31/3
-B/A = -7  dan  C/A = 31/3
-B/A = -21/3      C/A = 31/3
A = 3, B = 21, C = 31
Ax² + Bx + C = 0  maka pers.
3x² + 21x + 31 = 0

(c.)  ¼α dan ¼β
¼α + ¼β = -B/A
¼(α + β) = -B/A
¼(-1) = -B/A
-¼ = -B/A
-B/A = -1/4
¼α(¼β) = C/A
(¼)² αβ = C/A
¹/₁₆ αβ = C/A
¹/₁₆ (-5/3) = C/A
C/A = -5/48
-B/A = -1/4  dan  C/A = -5/48
-B/A = -12/48      C/A = -5/48
A = 48, B = 12, C = -5
Ax² + Bx + C = 0  maka pers.
48x² + 12x - 5 = 0

(d.)  2α+3 dan 2β+3
(2α+3) + (2β+3) = -B/A
2α + 2β + 6 = -B/A
2(α + β) + 6 = -B/A
2(-1) + 6 = -B/A
-2 + 6 = -B/A
-B/A = 4
(2α+3)(2β+3) = C/A
4αβ + 6α + 6β + 9 = C/A
4αβ + 6(α + β) + 9 = C/A
4(-5/3) + 6(-1) + 9 = C/A
(-20/3) - 6 + 9 = C/A
(-20/3) + 3 = C/A
(-20/3) + (9/3) = C/A
C/A = -11/3
-B/A = 4       dan  C/A = -11/3
-B/A = -12/(-3)      C/A = 11/(-3)
A = -3, B = 12, C = 11
Ax² + Bx + C = 0  maka pers.
-3x² + 12x + 11 = 0, atau
3x² - 12x - 11 = 0

(xcvi)