If x^3 + x^2 - ax +b is done divisible by (x^2 -x) find the values of a and b

a=2, b=0

Step-by-step explanation:

Given:

f(x) = x^3 + x^2 - ax +b is divisible by (x^2 -x)

Need to find:

Values of a and b.

Solution:

Factor

(x^2-x) = (x)(x-1)

if x^3 + x^2 - ax +b is divisible by (x)(x-1), then

both x and (x-1) are roots to f(x), therefore

x=0 or x=1 are roots to f(x).

Using the factor theorem,

f(x=0) = 0 => 0+0-0+b = 0 => b=0

f(x=1)=0 => 1+1-a+b=0 => 1+1-a+0 = 0  => a=2

That is a=2, b=0

Now factor f(x) with a=2, b=0

f(x) = x^3 + x^2 - ax +b

= x^3 + x^2 - 2x

= x (x^2 + x - 2)

= x (x+2) (x-1)

Thus both x and (x-1) are factors... checks.

  n=   0.0000 - 0.3750 i  

  n=   0.0000 + 0.3750 i

step-by-step explanation:

one of these should be correct