Question

x2 – ax3 + bx2 - cx +11. x2 – ax3 + bx2 - cx + 8 = 0 divided by (x -1) leaves a remainder of 4, divided by (x + 1) leaves a remainder 3, then b = (a) 2.5 (b) -5.5 (c) 3.5 (d) 6.5 8 = 0 divided by (x -1) leaves a remainder of 4, divided by (x + 1) leaves a remainder 3, then b =

Answer 1

Answer:

-5.5

Step-by-step explanation:

Answer 2

Answer:

The value of b is given in option (b), which is -5.5.

Step-by-step explanation:

Let the given polynomial be,

$f(x)=x^2-ax^3+bx^2-cx+8$

It is given that,

When the polynomial f(x) is divided by (x-1), the remainder will be 4.

When the polynomial f(x) is divided by (x+1), the remainder will be 3.

The value of b can be found by dividing the given polynomial by the divisors given and then solving the resulting equations.

Step 1 of 3:

Dividing the polynomial f(x) by (x-1), we get

$\frac{x^2-ax^3+bx^2-cx+8}{x-1} =-a+b-c+9$

(The steps for long division are given below.)

Equating with the given remainder 4,

$-a+b-c+9=4\\-a+b-c=-5$----- (1)

Step 2 of 3:

Dividing the polynomial f(x) by (x+1), we get

$\frac{x^2-ax^3+bx^2-cx+8}{x+1} =a+b+c+9$

(The steps for long division are given below.)

Equating with the given remainder 3,

$a+b+c+9=3\\a+b+c=-6$----- (2)

Step 3 of 3:

Solving the equations (1) and (2), we get

$-a+b-c=-5\\a+b+c=-6$

____________

        $2b=-11\\b=-\frac{11}{2} \\b=-5.5$

Final answer:

The value of b is -5.5.

This answer is given in option (b).

Hence, option (b) is correct.