The polynomial `f(x)=x^4+a x^3+b x^3+c x+d` has real coefficients and `f(2i)=f(2+i)=0.` Find the value of `(a+b+c+d)dot`

Options

A. 1
B. 4
C. 9
D. 10

Answer

3

Explanation

If a polynomial has real coefficients then roots occur in complex conjugate and roots are 2i -2i, 2 + I,2-I
Hence ,f(x)=(x+2i)(x-2e)(x-2-i)(x-2+I)`
`f(1)=(1+xi)(1-2i)(1-2-i)(1-2+i)`
`f(1)=5xx2=10`
Also, f(1)= 1+a+b+c+d`
`therefore 1+a+b+c+d=10`
`rArr a+b+c+d=9`