HOTS
The sum of the remainders obtained when (x + (k + 8) + k) is divided by (x - 2)
or when it is divided by (x + 1) is zero. Find the value of k.
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HOTS
The sum of the remainders obtained when (x + (k + 8) + k) is divided by (x - 2)
or when it is divided by (x + 1) is zero. Find the value of k.
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Answer:
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Step-by-step explanation:
Given :
Find :
Solution :
x³ + (k + 8)x + k
Put x = 2 to obtain first remainder
=> R¹ = (2)³ + (k + 8)² + k = 24 + 3k
Put x = –1 to obtain second remainder
=> R² = (–1)³ + (k + 8) + k = –9
So,
R¹ + R² = 0
=> 24 + 3k –9 = 0
=> 3k + 15 = 0
=> 3k = –15
=> k = –15/3
=> k = –5.
Hence :