Math, asked by siddhum3, 4 months ago

The product of the coefficients of quotient when f(x) = x4 - 3x² + x-1 is divided by (2x-1) is​

Answers

Answered by pushpanjalimoharana0
0

Answer:

A polynomial p(x) is defined as

⇒p(x)=g(x)q(x)+r(x)

where g(x)= divisor ; q(x)= quotient and r(x)= remainder

∴ p(x) can be found by multiplying g(x) with q(x) & adding r(x) to the product.

(i).g(x)=(x−2); q(x)=x

2

−x+1; r(x)=4

∴p(x)=(x−2)[x

2

−x+1]+4

=x

3

−x

2

+x−2x

2

+2x−2+4

=x

3

−3x

2

+3x+2

(ii).g(x)=(x+3); q(x)=2x

2

+x+5; r(x)=3x+1

∴p(x)=(x+3)[2x

2

+x+5]+(3x+1)

=2x

3

+x

2

+5x+6x

2

+3x+15+

3x+1

=2x

3

+7x

2

+11x+16

(iii).g(x)=(2x+1); q(x)=x

3

+3x

2

−x+1; r(x)=0

∴p(x)=(2x+1)[x

3

+3x

2

−x+1]+(0)

=2x

4

+6x

3

−2x

2

+2x+x

3

+3x

2

−x+1

=2x

4

+7x

3

+x

2

+x+1

(iv).g(x)=(x−1); q(x)=x

3

−x

2

−x−1; r(x)=2x−4

∴p(x)=(x−1)[x

3

−x

2

−x−1]+(2x−4)

=x

4

−x

3

−x

2

−x−x

3

+x

2

+x+1+2x−4

=x

4

−2x

3

+2x−3

(v).g(x)=(x

2

+2x+1); q(x)=x

4

−2x

2

+5x−7; r(x)=4x+12

∴p(x)=(x

2

+2x+1)[x

4

−2x

2

+5x−7]+(4x+12)

=x

6

−2x

4

+5x

3

−7x

2

+2x

5

+4x

3

+10x

2

−14x+x

4

−2x

2

+5x−7+4x+12

=x

6

−x

4

+x

3

+x

2

+2x

5

−5x+5

=x

6

+2x

5

−x

4

+x

3

+x

2

−5x+5

Hence, solve.

Answered by kedarerani43
0

Answer:

Haryanvi secure samajh mein

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