if the polynomials a x cube + 3 x square - 13 and 2 x cube minus 5 x + a when divided by x minus two leave same remainder find the value of a
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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.
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