CBSE Class 10 Answered

Apply apply division algorithm find quotient and remainder on dividing each of the following f x is equal to 4 x cube + 8 x + 8 x square + 7 x is equal to 2 x square minus x + 1

Asked by kalpeshbharwad898 | 06 May, 2020, 03:24: PM

Expert Answer

Given: f(x)=4x³+8x²+8x+7 and g(x)=2x²-x+1

To find the quotient q(x) and remainder r(x) when f(x) is divided by g(x) using division algorithm

Here, degree of q(x) must be degree of f(x) - degree of g(x) = 3-2 = 1

Degree of r(x) must be < degree of g(x) = 2

Therefore, degree of q(x) is 1 and degree of r(x) < 2

Let q(x)=ax+b and r(x)=cx+d

Using division algorithm, we have

f(x)=g(x)q(x)+r(x)

rightwards double arrow 4 x cubed plus 8 x squared plus 8 x plus 7 equals open parentheses 2 x squared minus x plus 1 close parentheses open parentheses a x plus b close parentheses plus open parentheses c x plus d close parentheses rightwards double arrow 4 x cubed plus 8 x squared plus 8 x plus 7 equals 2 a x cubed minus a x squared plus a x plus 2 b x squared minus b x plus b plus c x plus d rightwards double arrow 4 x cubed plus 8 x squared plus 8 x plus 7 equals 2 a x cubed plus x squared open parentheses 2 b minus a close parentheses plus x open parentheses a minus b plus c close parentheses plus b plus d E q u a t i n g space t h e space c o e f f i c i e n t s space o f space x cubed comma space x squared comma space x space a n d space c o n s tan t comma space w e space g e t 2 a equals 4 rightwards double arrow a equals 2 space... space left parenthesis i right parenthesis 2 b minus a equals 8 rightwards double arrow 2 b equals 8 plus a equals 10 rightwards double arrow b equals 5 space... space left parenthesis i i right parenthesis a minus b plus c equals 8 rightwards double arrow 2 minus 5 plus c equals 8 rightwards double arrow c equals 11 space... space left parenthesis i i i right parenthesis b plus d equals 7 rightwards double arrow d equals 7 minus 5 rightwards double arrow d equals 2 H e n c e comma space t h e space q u o t i e n t space i s space 2 x plus 5 space a n d space t h e space r e m a i n d e r space i s space 11 x plus 2.

Answered by Renu Varma | 07 May, 2020, 11:31: AM

CBSE Class 10 Answered

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