Jika p, q, r akar-akar persamaan x³ - x² + 2 = 0 tentukan nilai dari
[tex]\displaystyle \begin{vmatrix}p & q & r\\ q & r & p\\ r & p & q\end{vmatrix}[/tex]
[tex]\displaystyle \begin{vmatrix}p & q & r\\ q & r & p\\ r & p & q\end{vmatrix}[/tex]
Verified answer
ALJABAR
ax³ + bx² + cx + d = 0
x1 + x2 + x3 = -b/a
x1x2 + x2x3 + x3x1 = c/a
x1x2x3 = -d/a
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x³ - x² + 2 = 0
p + q + r = -(-1)/1 = 1
pq + qr + rp = 0/1 = 0
pqr = -2/1 = -2
soal
= 3pqr - (p³ + q³ + r³)
= -(p + q + r)(p² + q² + r² - (pq + qr + rp))
= -(1)((p + q + r)² - 2(pq + qr + rp) - 0)
= -1 . 1²
= -1