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When 2x^3 + ax^2 + bx –3 is divided by (x–1) and (x+2), the remainders are 8 and –7, respectively. Find a and b. ?
1 Answer
- 冷眼旁觀Lv 71 year agoFavorite Answer
Let f(x) = 2x³ + ax² + bx - 3
When 2x³ + ax² + bx - 3 is divided by (x – 1), the remainder is 8.
By Remainder Theorem: f(1) = 8
2(1)³ + a(1)² + b(1) - 3 = 8
a + b = 9 …… [1]
When 2x³ + ax² + bx - 3 is divided by (x + 2), the remainder is -7.
By Remainder Theorem: f(-2) = -7
2(-2)³ + a(-2)² + b(-2) - 3 = -7
4a - 2b = 12
2a - b = 6 …… [2]
[1] + [2]:
3a = 15
a = 5
Substitute a = 5 into [1]:
(5) + b = 9
b = 4
Ans: a = 5 and b = 4