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Question
When x3−2x2+ax−b is divided by x2−2x−3, the remainder is x−6. The values of a and b are respectively :
When x3−2x2+ax−b is divided by x2−2x−3, the remainder is x−6. The values of a and b are respectively :
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Solution
The correct option is D −2 and 6
x3−2x2+ax−b is divided by x2−2x−3 and the remainder obtained is x−6.
Now, the first term in the quotient will be x since the coefficient of x3 is 1.
So, x(x2−2x−3)=x3−2x2−3x, which when subtracted from the dividend gives (a+3)x−b
Since the degree of the above term is less than the divisor, it is the remainder and so we equate it to x−6
Hence, a+3=1 and b=6
⇒a=−2,b=6
x3−2x2+ax−b is divided by x2−2x−3 and the remainder obtained is x−6.
Now, the first term in the quotient will be x since the coefficient of x3 is 1.
So, x(x2−2x−3)=x3−2x2−3x, which when subtracted from the dividend gives (a+3)x−b
Since the degree of the above term is less than the divisor, it is the remainder and so we equate it to x−6
Hence, a+3=1 and b=6
⇒a=−2,b=6
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