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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CBSE Class 10 Answered

Application Videos

HCF of given two numbers

Euclid's Division Lemma

Concept Videos

Euclid's Division Lemma and Algorithm ...

Euclid's Division Lemma and Algorithm

Euclid's Division Lemma and Algorithm

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