Question

If f(x) = x³ + x² - ax + b is divisible by x² - x
then find the values of a and b.​

Answer 1

Step-by-step explanation:

X³ + x² -ax + b is divisible by x² - x or x(x -1)

it means x and (x -1) are the factors of x³ + x² -ax + b .

hence,. 0 and 1 are the zeros of x³ + x² -ax + b.

put x = 0

(0)³ + (0)² -a(0) + b = 0 => b = 0

put x = 1

(1)³ + (1)² - a(1) + b = 0

1 + 1 - a + b = 0

2 - a + 0 = 0 { after putting b = 0

a = 2

hence, a = 2 and b = 0

this answer is credited to @abhi178