Question 1100423
Polynomials with complex roots and real coefficients must have complex roots as complex conjugate pairs.
So if {{{11+i}}} is a root, so is {{{11-i}}}.
{{{f(x)= (x-(11+i))(x-(11-i))(x+2)(x-1) (x-a)}}}
You don't know what {{{a}}} is but we will get it using the point (0,8).
{{{f(x)=(x^2-22x+122)(x^2+x-2)(x-a)}}}
{{{f(x)=(x^4-21x^3+98x^2+166x-244)(x-a)}}}
So when {{{x=0}}},
{{{8=(0-0+0+0-244)(-a)}}}
{{{a=8/244}}}
{{{a=2/61}}}
{{{f(x)=(x^4-21x^3+98x^2+166x-244)(x-2/61)}}}
{{{highlight_green(f(x)=(61x^5-1283x^4+6020x^3+9930x^2-15216x+488)/61)}}}