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

Answer:

hope it is helpful and thank you for your

question

Answer 2

Answer:

Value of a and b is -23 and -46 respectively.

Step-by-step explanation:

Given,

$f(x) = {x}^{3} + a {x}^{2} - bx - 8$

Now, f[x]=x³+ax²-bx-8 is divided by x-2 the remainder is 0.

So, if we put x=2 then f(x) will be 0.

$f(2) = {2}^{3} + a \times {2}^{2} - b \times 2 - 8 = 0 \\ 8 + 4a - 2b - 8 = 0 \\ 2a - b = 0....(1)$

Again it is given that when f(x) divided by x-1 the remainder is -30.

So,

$f(1) + 30 = 0 \\ {1}^{3} +a \times {1}^{2} - b \times 1 - 8 + 30 = 0 \\ 1 +a - b - 8 + 30 = 0 \\ a - b - 23 = 0...(2)$

We are subtracting equation (2) from equation (1),

$2a -b -a + b +23 = 0 \\ a = -23$

We are putting value of a in equation (1),

$b = +2a \\ = 2 \times ( -23) \\ = -46$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

#SPJ3