Question

If x^3+x^2-ax+b is divisible by x^2-x find a and b

Answer 1

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

Hope this helps!