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Q.

If (x + a) is a factor of the polynomial 2 x 2 +2ax+5x+10 , then find the value of a.


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a

3

b

2

c

5

d

7 

answer is B.

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Detailed Solution

Given that (x + a) is a factor of the polynomial 2 x 2 +2ax+5x+10 .
As per the remainder theorem, when dividing a polynomial f(x) by a linear polynomial say (x – a), if the remainder is obtained as f(a) such that f(a) = 0, then (x – a) is termed as the factor of the polynomial f(x).
Now, as (x + a) is a factor of the given polynomial, then by remainder theorem, we have,
x+a=0 x=−a
So, f(−a)=0 .
So, we have,
f(−a)=0 2 (−a) 2 +2a(−a)+5(−a)+10=0 2 a 2 −2 a 2 −5a+10=0 −5a+10=0 −5a=−10 a= −10 −5 a=2
So, the value of a is obtained as 2.
Hence, the correct option is (2).
         
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