If the remainder of the polynomial a0 + a1x + a2x2 + ....... + anxn wh

1.	If the remainder of the polynomial a0 + a1x + a2x2 + ....... + anxn when divided by (x – 1) is 1, then which one of the following is correct ?(a) a0 + a2 + ...... = a1 + a3 + ...... (b) a0 + a2 + ...... = 1 + a1 + a3 + ...... (c) 1 + a0 + a2+ ...... = – (a1 + a3 + ......) (d) 1 – a0 – a2 – ...... = a1 + a3 + ......
Answer» (d) 1 – a₀ – a₂ – ...... = a₁ + a₃ + ...... Let f(x) = a₀ + a₁x + a₂x² + ......... + a_nxⁿ Given, f(1) = 1 ⇒ a₀ + a₁ + a₂ + ........ + a_n = 1 ⇒ 1 – a₀ – a₂ – ........ = a₁ + a₃ + ........ .

If the remainder of the polynomial a0 + a1x + a2x2 + ....... + anxn when divided by (x – 1) is 1, then which one of the following is correct ?(a) a0 + a2 + ...... = a1 + a3 + ...... (b) a0 + a2 + ...... = 1 + a1 + a3 + ...... (c) 1 + a0 + a2+ ...... = – (a1 + a3 + ......) (d) 1 – a0 – a2 – ...... = a1 + a3 + ......

Answer»

(d) 1 – a₀ – a₂ – ...... = a₁ + a₃ + ......

Let f(x) = a₀ + a₁x + a₂x² + ......... + a_nxⁿ

Given, f(1) = 1

⇒ a₀ + a₁ + a₂ + ........ + a_n = 1

⇒ 1 – a₀ – a₂ – ........ = a₁ + a₃ + ........ .