Question

if the polynomials2x^3+ax^2+3x-5 and x^3+x^2-4x+a leave the same remainder when divided by x-2, find the value of a.


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Answer 1

Answer:

Hey Friend ☺

Let p ( x ) = 2x^3 + ax^2 + 3x - 5

q ( x ) = x^3 + x^2 - 2x + a

Using remainder theorem,.

P ( 2 ) will be the remainder when p ( x ) is divided by x - 2

So

p ( 2 ) = 2x^3 + ax^2 + 3x - 5

= 2 ( 2 )^3 + a( 2 )^2 + 3 ( 2 ) - 5

= 2 × 8 + 4a + 6 - 5

= 4a + 16 + 1

= 4a + 17

Similarly q ( 2 ) will be the remainder when q ( x ) is divided by x - 2 .

q ( 2 ) = x^3 + x^2 - 2x + a

= ( 2 )^3 + ( 2 )^2 - 2 ( 2 ) + a

= 8 + 4 - 4 + a

= a + 8

Two remainders are equal so we get equation,

4a + 17 = a + 8

》4a - a = - 17 + 8

》3a = - 9

》a = - 9/3

》a = - 3

Hope it helps you ..!!

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