Question

when (x3-2x2+px-q)is is divided by (x2-2x-3),THE remainder is (x-6).Find the value of p and q.

Answer 1

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When (x3-2x2+px-q)is is divided by (x2-2x-3),THE remainder is (x-6).Find the value of p and q.




anѕwer:



Given;


We need to find the value of p and q


Let,


f( x ) = x³ - 2x² + px - q


q( x ) = x² - 2x -3

r ( x ) =x - 6



So;

(x² - 2x - 3) by doing hcf (long divison method) of (x³ - 2x² + px - q)


We get ;


Remainder = x (p+3) - q = r (x)


Hence, we get


x ( p + 3) - q = x - 6


Comparing the coefficient on both the sides, we get ;


p +3 = 1


p = -2

q = 6



Hence the value of p and q are -2 and 6



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Answer 2

Answer:ANSWER

x

3

−2x

2

+ax−b is divided by x

2

−2x−3 and the remainder obtained is x−6.

Now, the first term in the quotient will be x since the coefficient of x

3

is 1.

So, x(x

2

−2x−3)=x

3

−2x

2

−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