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標題:
number and algebra
發問:
When 3x^3 + 4x^2 + ax + b is divided by x + 1 and x - 2 , the remainders are 4 and 28 respectively. Find the values of a and b. 詳細!
最佳解答:
Let f(x) = 3x^3 + 4x^2 + ax + b By Remainder Theorem, when f(x) is divided by x+1, the remainder is f(-1). Therefore, 4 = f(-1) = 3(-1)^3 + 4(-1)^2 + a(-1) + b 4 = -3 + 4 - a + b a - b = -3 --------------------(1) By Remainder Theorem again, when f(x) is divided by x-2, the remainder is f(2). Therefore, 28 = f(2) = 3(2)^3 + 4(2)^2 + a(2) + b 28 = 24 + 16 + 2a + b 2a + b = -12 --------------------(2) (1)+(2): 3a = -15. So a = -5. Substitute into (1), -5 - b = -3. So b = -2. In conclusion, a = -5, b = -2 Hope it helps! ^^
其他解答:
number and algebra
發問:
When 3x^3 + 4x^2 + ax + b is divided by x + 1 and x - 2 , the remainders are 4 and 28 respectively. Find the values of a and b. 詳細!
最佳解答:
Let f(x) = 3x^3 + 4x^2 + ax + b By Remainder Theorem, when f(x) is divided by x+1, the remainder is f(-1). Therefore, 4 = f(-1) = 3(-1)^3 + 4(-1)^2 + a(-1) + b 4 = -3 + 4 - a + b a - b = -3 --------------------(1) By Remainder Theorem again, when f(x) is divided by x-2, the remainder is f(2). Therefore, 28 = f(2) = 3(2)^3 + 4(2)^2 + a(2) + b 28 = 24 + 16 + 2a + b 2a + b = -12 --------------------(2) (1)+(2): 3a = -15. So a = -5. Substitute into (1), -5 - b = -3. So b = -2. In conclusion, a = -5, b = -2 Hope it helps! ^^
其他解答:
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