Tentukan Penyelesaian sistem persamaan kuadrat berikut x-8x+15=0

Tentukan Penyelesaian sistem persamaan kuadrat berikut x-8x+15=0

Jawaban yang benar adalah x = 3 atau x = 5

Asumsi soal:
x² – 8x + 15 = 0

Ingat kembali:
Untuk menyelesaikan persamaan kuadrat dapat dilakukan dengan:
1. Metode pemfaktoran
2. Metode melengkapkan kuadrat sempurna
3. Metode rumus kuadratik atau rumus abc

Untuk soal di atas akan diselesaikan menggunakan metode pemfaktoran.
Memfaktorkan persamaan kuadrat adalah mengubah persamaan kuadrat tersebut menjadi bentuk perkalian.
x² + bx + c = 0
(x + p)(x + q) = 0
p + q = b
pq = c

x² – 8x + 15 = 0
➡️ –8 = –5 + (–3)
➡️ 15 = (–5)(–3)

x² – 8x + 15 = 0
{x + (–5)}{x + (–3)} = 0
(x – 5)(x – 3) = 0
x – 5 = 0
x = 0 + 5
x = 5
atau
x – 3 = 0
x = 0 + 3
x = 3

Jadi, penyelesaian persamaan kuadrat di atas adalah x = 3 atau x = 5

 

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