Question

If the polynomial 2x3 + ax2 + 3x ? 5 and x3 + x2 ? 4x + a leave the same remainder when divided by x - 2, Find the value of a.

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Answer 1

Answer:

a=2x3 + ax2 + 3x ? 5 and x3 + x2 ? 4x + a leave the same

Answer 2

a = -13/3

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.