Question

if the polynomial 2x 3 +ax2 +3x-5 and x3+x2-4x+a leaves the same remainder when divided by x-2 ,find the value of a

Answer 1

Solution-
Let the given polynomials be f(x) and g(x).
When f(x) and g(x) are divided by (x-2) they leave the same remainder.

I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)

So that,

f(2) = g(2)

2x³+ax²+3x-5 = x³+x²-4x+a

2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a

2(8)+a(4)+6-5 = 8+4-8+a

16+4a+1 = 4+a

17+4a = 4+a

4a-a = 4-17

3a = -13

a = -13/3.

Answer 2

Step-by-step explanation:

Let the given polynomials be f(x) and g(x).

ATQ, 

When f(x) and g(x) are divided by (x-2) they leave the same remainder.

I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)

So that,

f(2) = g(2)

→2x³+ax²+3x-5 = x³+x²-4x+a

→2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a

→2(8)+a(4)+6-5 = 8+4-8+a

→16+4a+1 = 4+a

→17+4a = 4+a

→4a-a = 4-17

→3a = -13

→a = -13/3.

Hope helped!

:)