Question

已知代数式ax²+px+q,当x=-1时,它的值是0;当x=-2时,它的值是5;当x=3时,它的值是-15，则a、p、q=

Answer 1

a-p+q=0 (1)
4a-2p+q=5 (2)
9a+3p+q=-15 (3)
(2)-(1)得
3a-p=5 (4)
(3)-(2)得
5a+5p=-20
a+p=-4 (5)
解方程组(4)(5)得
a=1/4
p=-17/4
把a=1/4，p=-17/4代入(1)得
q=-9/2

追问

确定对么？

追答

对的

Answer 2

(1)a-p+q=0
(2)4a-2p+q=5
(3)9a+3p+q=-15
(2)-(1)
(4)3a-q=5
(3)-(2)
5a+5p=-20
(5)a+p=-4
(4)+(5)
4a=1 a=1/4 p=-17/4 q=-9/2

Answer 3

a=1/4 p=-17/4 q=-9/2