Question

if the polynomials 2x Cube + ax square + 3 x minus 5 and x cube + x square - 2 X + a leave the same remainder when divided by x minus 2 find the value of a​

Answer 1

Answer:

The value of a is -3

Step-by-step explanation:

$\textsf{Let}$

$\mathsf{p(x)=2x^3+ax^2+3x-5}$

$\mathsf{q(x)=x^3+x^2-2x+a}$

$\textsf{when p(x) is divided by (x-2), the remainder is p(2)}$

$\mathsf{=2(2)^3+a(2^)2+3(2)-5}$

$\mathsf{=16+4a+6-5}$

$\mathsf{=17+4a}$

$\textsf{when q(x) is divided by(x-2), the remainder is q(2)}$

$\mathsf{=2^3+2^4-2(2)+a}$

$\mathsf{=8+4-4+a}$

$\mathsf{=8+a}$

$\textsf{As per given data, p(2)=q(2)}$

$\implies\mathsf{17+4a=8+a}$

$\implies\mathsf{9=-3a}$

$\implies\boxed{\mathsf{a=-3}}$

Answer 2

Answer:

a=-3

Step-by-step explanation:

Let

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

q(x)=x^3+x^2-2x+9

when p(x) is divided by (x-2(,the remainder isi(2)

=2^3+2^4-2(2)+9

8+4-4+9=8+a

As per given data,p(2)=9(2)

=17+49=8+9

=9=-3a

a=-3