Jawab:
(a.) k+m = -4
(b.) km = 5
(c.) 1/k + 1/m = -⁴/₅
(d.) k²+m² = 6
(e.) k²-m² = {-8i, 8i}
(f.) k - m = ±2i

Penjelasan dengan langkah-langkah:
Diketahui pers. kuadrat
3x² + 12x + 15 = 0, bisa disederhanakan
(3÷3)x² + (12÷3)x + (15÷3) = 0
x² + 4x + 5 = 0
TEORI VIETA:
x² + (-(k+m))x + km = 0
x² + 4          x + 5 = 0

Maka (a.) -(k+m) = 4
--> k+m = -4

(b.) km = 5

(c.) 1/k + 1/m = (k+m)/km
= -⁴/₅

(d.) k²+m² = (k+m)²-2km
= (-4)²-2(5) = 16-10
= 6

(f.) k - m
x² + 4x + 5 = 0
a = 1, b = 4, c = 5
x = -b±√(b²-4ac) ÷ 2a
x = -4±√(4²-4(1)(5)) ÷ 2(1)
x = -4±√(16-20) ÷ 2
x = -4±√(-4) ÷ 2
x = -4±(√4)i ÷ 2
x = -4±2i ÷ 2
x = -2±i
k = -2+i, m = -2-i
k - m = {-2+i-(-2-i), -2-i-(-2+i)}
= {-2+i+2+i, -2-i+2-i}
= {2i, -2i}
= ±2i

(e.) k²-m² = (k+m)(k-m)
= -4(±2i) = {-4(2i), -4(-2i)}
= {-8i, 8i}

(xcvi)