2. If Px) 2x3+ax3x 5 and Q(x)xx2- 4x + a leave the same remainderx3+x2

1.	2. If Px) 2x3+ax3x 5 and Q(x)xx2- 4x + a leave the same remainderx3+x2-4x + a leave the same remainderwhen divided by (x - 2), find a?
Answer» 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.

2. If Px) 2x3+ax3x 5 and Q(x)xx2- 4x + a leave the same remainderx3+x2-4x + a leave the same remainderwhen divided by (x - 2), find a?

Answer»

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.