If x3 + x2 - ax + b is divisible by (x2 -x),write the value of a and b

1.	If x3 + x2 - ax + b is divisible by (x2 -x),write the value of a and b.
Answer» Equating x² – x to 0 to find the zeroes, we will get x(x – 1) = 0 ⇒ x = 0 or x – 1 = 0 ⇒ x = 0 or x = 1 Since, x³ + x² – ax + b is divisible by x² – x. Hence, the zeroes of x² – x will satisfy x³ + x² – ax + b ∴ (0)³ + 0² – a(0) + b = 0 ⇒ b = 0 And (1)³ + 1² – a(1) + 0 = 0 [∵b = 0] ⇒ a = 2

If x3 + x2 - ax + b is divisible by (x2 -x),write the value of a and b.

Answer»

Equating x² – x to 0 to find the zeroes,

we will get

x(x – 1) = 0

⇒ x = 0 or x – 1 = 0

⇒ x = 0 or x = 1

Since,

x³ + x² – ax + b is divisible by x² – x.

Hence,

the zeroes of x² – x will satisfy x³ + x² – ax + b

∴ (0)³ + 0² – a(0) + b = 0

⇒ b = 0

And

(1)³ + 1² – a(1) + 0 = 0 [∵b = 0]

⇒ a = 2