Jawaban:
Diketahui rumus :
(a)x2+(b)x+c
x2– (p + q)x + pq
Dari x2 – 5x – 1 = 0
diketahui a = 1, b = -5, c = -1
Maka:
p + q = -b/a
p + q = - (-5)/1
p + q = 5
pq = c/a
pq = -1/1
pq = -1
(2p + 1) + (2q + 1)
= 2(p + q) + 2
= 2 × 5 + 2 = 12
(2p + 1)(2q + 1)
= 4pq + 2(p + q) + 1
= 4(–1) + 2(5) + 1 = 7
Jadi, persamaan kuadrat yang baru :
x2 – 12x + 7 = 0