Question

the polynomial a x power 3 + 3 x power 2 - 13 and 2 x power 3 minus 5 x + 8 divided by X + 2 if the remainder in each case is same find the value of a​

Answer 1

Answer:

Taking the polynomials as p(x)=ax3+3x2-13 and the other polynomial as q(x)=2x3-5x+a.

If we divide both of the polynomials by (x-2) they will give the same remainder as c.

On taking p(2)=R.

Then the value of a(2)3+3(2)2-13=R.

8a+12-13=R.

8a-1=R ....(1).

While again taking q(2)=R.

Then we will get 2(2)3-5(2)+a=R.

16-10+a=R.

6+a=R ...(2).

On substituting the values of the equation we will get .

8a-1=6+a.

7a=7.

And finally the value of a=1.