Question

Using factor theorem, find the value of 'a' if the polynomial p(x) = 2x4 - ax3 + 4x2 - x + 2 is divisible by (2x + 1).​

Answer 1

Answer: given , p(x)= 2x4- ax3+4x2-x+2 and (2x+1) is divisible by p(x) , so its remainder will be zero

Now by using remainder theorem we have, x=-1/2

p(-1/2)=2(-1/2)4- a(-1/2)3+4(-1/2)2 -(-1/2)+2=0

-4 +3a/2 -4+1/2+2=0

-8+ (3a+1)/2+2=0

-6+(3a+1)/2=0

(3a+1)= 6×2

a =11/3