Question

Divide
$f(x) = {x}^{4} + 2 {x}^{3} - 2 {x}^{2} + x - 1$
$g(x) = {x}^{2} + 2x - 3$
​

Answer 1

Answer:

f(x)=4x

3

+3x

2

−12ax−5

g(x)=2x

3

+ax

2

−6x−2

f(x) when divided by (x−1) leaves remainder as R

1

g(x) when divided by (x−2) leaves remainder as R

2

Therefore, according to Remainder theorem,

f(1)=4(1)

3

+3(1)

2

−12a(1)−5

=4+3−12a−5

=2−12a=R

1

⟶(1)

Similarly,

g(2)=2(2)

3

+a(2)

2

−6(2)−2

=16+4a−12−2

=2+4a=R

2

⟶(2)

Also, 3R

1

+R

2

−28=0

∴3(2−12a)+2+4a−28=0

⇒6−36a+2+4a−28=0

⇒32a=−20

⇒

a=

8

−5

Answered By

Rehaman andhra Pradesh