Question

If x^3 + 3x^2 − ax + 3 is exactly divisible by (x−2) , then the value of 'a' is

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Answer 1

Question -

If x³+3x²-ax+3 is exactly divisible by (x-2) then find the value of 'a'

Solution -

Given,

x³+3x²-ax+3 is exactly divisible by (x-2)

Therefore,

x-2=0

x= 2

Let, p(x) = x³+3x²-ax+3

Putting the value of x = 2 we will get -

p(2)= (2)³+3(2)²-a(2)+3

p(2)= 8+12-2a+3

p(2) = 23-2a

Since,x³+3x²-ax+3 is a factor of (x-2)

Therefore ,remainder =0

=>23-2a=0

=>23=2a

=> a= 23/2

Therefore the value of a is 23/2