Question 571036
The conjugate of -2-5i is -2+5i. We first get a quadratic equation having -2-5i and -2+5i as roots.
sum = (-2-5i) + (-2+5i) = -4
product = (-2-5i)(-2+5i) = 29
{{{x^2- (sum)x + product = 0}}}
The quadratic equation is  {{{x^2 + 4x + 29 = 0}}}

Next, we get the quadratic equation having 5 as a double root.

The quadratic equation is {{{(x-5)^2 = 0}}}

We multiply the two quadratic equations to get the polynomial of degree 4.

{{{(x^2 + 4x + 29)*(x-5)^2 = 0}}}

{{{x^4 -6x^3 +14x^2 -190x + 725 = 0}}}

Answer: {{{x^4 -6x^3 +14x^2 -190x + 725 = 0}}}