Question

pls tell the ans

WITH PROCESS

Answer 1

Answer:

Option C

Step-by-step explanation:

Given :-

(x+1)⁷ = a7x⁷+a6x⁶+a5x⁵+...+a1x+a0

To find:-

Find the value of a0+a1+a2+...+a7 ?

Solution :-

Given 7th degree polynomial in the variable x is

a7x⁷+a6x⁶+a5x⁵+...+a1x+a0

Where a0,a1,...,a7 are the coefficients

It is defined as

(x+1)⁷ = a7x⁷+a6x⁶+a5x⁵+...+a1x+a0

Put x = 1 then

(1+1)⁷ = a7(1)⁷+a6(1)⁶+a5(1)⁵+...+a1(1)+a0

=> 2⁷ = a7(1)+a6(1)+a5(1)+...+a1+a0

=> 2⁷ = a7+a6+a5+...+a1+a0

Since 2⁷ = 2×2×2×2×2×2×2 = 128

=> 128 = a7+a6+a5+...+a1+a0

=> a7+a6+a5+...+a1+a0 = 128

=> a0+a1+a2+a3+...+a7 = 128

Answer:-

The value of a0+a1+a2+a3+...+a7 for the given problem is 128

Points to know:-

• If (x-1) is a factor of P(x) then P(a) = 0.
• If the sum of the coefficients is zero then 1 is the zero of the P(x) .