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Let P(x)=x^3+ax^2+bx+15.When P(x) is divided by x-3,the remainder is 66.When P(x) is divided by x+3,the remainder is 0.Find the values of a and b.
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2008-04-20 5:20 am
Let P(x)=x3+ax2+bx+15.When P(x) is divided by x-3,the remainder is 66.When P(x) is divided by x+3,the remainder is 0.Find the values of a and b.
回答 (1)
2008-04-20 5:41 am
✔ 最佳答案
P(x)=x^3 ax^2 bx 15By remainder theorem,
P(3) = 66
P(-3)= 0
P(3) = 3^3 + a(3)^2 + b(3) +15
27 + 9a + 3b + 15 = 66
9a + 3b = 24
3a + b = 8 ... (1)
P(-3) = (-3)^3 + a(-3)^2 + b(-3) +15
-27 + 9a - 3b + 15 = 0
9a - 3b - 12 = 0
3a -b - 4 = 0
3a - b = 4 ... (2)
(1) + (2)
6a = 12
a = 2
put b = 2 into (2)
3(2) - b = 4
6 - b = 4
b = 2
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