Question

2x^3+7x^2+x-6 in x+2 are​

Answer 1

Answer:

a=10

Step-by-step explanation:

Let f(x)=2x

3

−7x

2

+ax−6

Put x−2=0

⇒x=2

When f(x) is divided by (x−2), remainder =f(2)

∴f(2)=2(2)

3

−7(2)

2

+a.2−6

=2.8−7.4+2a−6

=16−28−6+2a

=2a−18

Let g(x)=x

3

−8x

2

+(2a+1)x−16

when g(x) is divided by (x−2) remainder =g(2)

∴g(2)=(2)

3

−8(2)

2

+(2a+1)2−16

=8−32+4a+2−16

=4a−38

By the condition we have

f(2)=g(2)

2a−18=4a−38

4a−2a=38−18

2a=20

a=

2

20

a=10

∴ Thus, the value of a=10