Question 1041825
Real coefficients means complex roots come in complex conjugate pairs.
{{{f(x)=a(x-i)(x+i)(x-(1-2i))(x-(1+2i))(x+4)}}}
{{{f(x)=a(x^2+1)(x^2-2x+5)(x+4)}}}
So when,
{{{x=0}}},
{{{f(0)=a(1)(5)(4)}}}
{{{40=a(20)}}}
{{{a=2}}}
So,
{{{f(x)=2(x^2+1)(x^2-2x+5)(x+4)}}}
{{{highlight(f(x)=2x^5+4x^4-4x^3+44x^2-6x+40)}}}