This is the isosceles right triangle, the diagonal of a square, the thing that so upset the Pythagoreans. The two sides and diagonal of a square are in ratio
so we get

We could have also gotten this using Trig:


Or by recognizing u=v because remaining angle is 45 so this must be isosceles so



Answer:
The first option
.
Step-by-step explanation:
To have exactly 2 real and two non real solutions, the degree of the polynomial must be a degree 4. Degree is the highest exponent value in the polynomial and is also the number of solutions to the polynomial. This polynomial ha 2 real+2 non real= 4 solutions and must be
. This eliminates the bottom two solutions.
In order to have two real and two non real solutions, the polynomial must factor. If it factors all the way like

This means x=0, 10, -10 are real solutions to the polynomial. It has no non real solutions. This eliminates this answer choice.
Only answer choice 1 meets the requirement.
2nd degree with real coefients
so if a+bi is a root then a-bi is also a root
if 2+i is a root then 2-i is also a root
so, the factored form of a quadratic equation with roots r1 and r2 is
(x-r1)(x-r2)
so
2+i and 2-i
(x-(2+i))(x-(2-i))
(x-2-i)(x-2+i)
expanding we get
x²-4x+5
so c=5