Finding a polynomial equation when given two points?

Let (a, b) is an arbitrary point which satisfies the condition.

2√[(b - (-3))^2 + (a - (-1))^2] = √[(b - (-8))^2 + (a - 5)^2] (Pythagorean Theorem)
4[(b + 3)^2 + (a + 1)^2] = (b + 8)^2 + (a - 5)^2
4[b^2 + 6b + 9 + a^2 + 2a + 1] = b^2 + 16b + 64 + a^2 - 10a + 25
4b^2 + 24b + 36 + 4a^2 + 8a + 4 = b^2 + 16b + 64 + a^2 - 10a + 25
3b^2 + 8b + 40 - 64 - 25 + 3a^2 + 18a = 0
3a^2 + 18a + 3b^2 + 8b - 49 = 0
a^2 + 6a + b^2 + (8/3)b - 49/3 = 0
(a + 3)^2 + (b + 4/3)^2 = 49/3 + 9 + 16/9
(a + 3)^2 + (b + 4/3)^2 = 244/9

your question is assume to say ; 2 roots of a polynomial equation with actual coefficients are 2 + 3i and ?7. discover 2 further roots. Then discover the degree of the polynomial. you disregarded the ?7 .