Question

If the polynomial P(x) x^1000 + ax + 9 is divisible by (x+1) , the a equals to :-

Answer 1

here is your answer....

Answer 2

Given,

p(x) = x^1000+ax+9

This polynomial is divisible by (x+1).

To find,

The value of a.

Solution,

The value of a will be 10.

We can easily solve this problem by following the given steps.

According to the question,

p(x) = x^1000+ax+9 is divisible by (x+1).

So, it means that the value of x will be given as follows:

(x+1) = 0

x = -1 ( Moving 1 from the left-hand side to the right-hand side results in the change of the sign from plus to minus.)

Now, this value of x should the given polynomial zero.

p(x) = x^1000+ax+9

(-1)^1000 +a(-1) +9 = 0

1-a+9 = 0 [The value of (-1)^1000 is 1 because 1000 is an even number. So, the product will be positive.]

-a+10 = 0

-a = -10

a = 10

Hence, the value of a is 10.