Question

If x3+x2-ax+b is divisible by x2-x find the value of 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

Answer 2

Hi Friend,

Here is your answer,

x³ + x² -ax + b is divisible by x² - x or x(x -1) 

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

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

PUTTING x = 0

(0)³ + (0)² -a(0) + b = 0 = b = 0


putting x = 1 

(1)³ + (1)² - a(1) + b = 0
1 + 1 - a + b = 0
2 - a + 0 = 0 
a = 2 

HERE IS YOUR ANSWER, a = 2 and b = 0


Hope it helps you!