If f(x) = x3 + x2 – ax + b is divisible by x2 – x write the values

1.	If f(x) = x3 + x2 – ax + b is divisible by x2 – x write the values of a and b.
Answer» a = 2, b = 0 Given, A polynomial f(x) = x³ + x² – ax + b Which is divisible by x² – x Now, x ² – x = (x – 1) = (x – 0)(x – 1) (x – 0) and (x – 1) are factors of polynomial f(x) ⇒ f(0) = 0 ⇒ 0³ + 0 – a × 0 + b = 0 ⇒ b = 0 And f(1) 1³+ 1 – a × 1 + b = 0 ⇒ 2 – a = 0 ⇒ a = 2 ∴ a = 2 and b = 0

If f(x) = x3 + x2 – ax + b is divisible by x2 – x write the values of a and b.

Answer»

a = 2, b = 0

Given,

A polynomial

f(x) = x³ + x² – ax + b

Which is divisible by x² – x

Now,

x ² – x = (x – 1) = (x – 0)(x – 1)

(x – 0) and (x – 1) are factors of polynomial f(x)

⇒ f(0) = 0

⇒ 0³ + 0 – a × 0 + b = 0

⇒ b = 0

And f(1)

1³+ 1 – a × 1 + b = 0

⇒ 2 – a = 0

⇒ a = 2

∴ a = 2 and b = 0