Question

when f[x]=x3+ax2-bx-8 is divided by x-2the remainder is 0 and when divided by x-1 the remainder is -30.find the value of a and b​

Answer 1

To Find:-

• Value of a & b

Given:-

• x-2 is a factor of f(x)=x³+ax²-bx-8
• when x-1 is divided by the same, remainder is -30

Answer:

A= 23

B= 46

Step-by-step explanation:

x-2 is a factor of f(x)=x³+ax²-bx-8

x-2=0

x=2

f(2)=0

2³+a(2)²-b(2)-8=0

8+a(4)-2b-8=0

4a-2b=0

4a=2b

a=(2b)/4. (Eq. 1)

Also when x-1 will have a remainder of -30 when divided by x³+ax²-bx-8

x-1=0

x=1

f(1)=1³+a(1)²-b(1)-8= -30

we know from (Eq.1)

1+[(2b)/4]-b-8=-30

(2b-4b)/4-7= -30

-2b/4= -30+7= -23

-2b= -23×4= -92

b= -92 ÷ -2= 92÷2= 46

b=46

Therefore value of b=46

Now to find value of a

From (Eq. 1)

a= (2b)/4

a=(2×46)/4

a=92/4

a=23

Verification:-

In the first case of x-2

when it's divided by

f(x)=x³+ax²-bx-8

result is 0

f(2)=2³+23(2)²-46(2)-8=0

8+23(4)-92+8=0

92-92=0

0=0

L.H.S=R.H.S

Now,in the second case,x-1 leaves a remainder of -30

when divided by f(x)=x³+ax²-bx-8

f(1)=1³+23(1)²-46(1)-8=-30

1+23(1)-46-8= -30

1+23-46-8= -30

24-54= -30

-30= -30

L.H.S=R.H.S

hence verified

Answer 2

Answer:

a=23, b=46

Step-by-step explanation:

The detailed answer is provided in the pics above