The number of polynomials of the form `x^(3)+ax^(2)+bx+c` that are divisible by `x^(2)+1`, where `a, b,cin{1,2,3,4,5,6,7,8,9,10}`, is

Options

A. 10
B. 15
C. 5
D. 8

Answer

A

Explanation

We have `i^(3)+ai^(2)+bi+c=0`
and `(-i)^(3)+a(-i)^(2)+b(-i)+c=0`
`implies(c-a)+(b-1)i=0`
and `(c-a)-i(b-1)+0`
`impliesb=1,a=c`
thus, total number of such polynomials`=.^(10)C_(1)=10`