Find two quadratic equations having the given solutions. (There are many correct answers. Use x for the variable. Enter your answers as a comma-separated list of equations.)

Question

4+5√(5), 4-5√(5)

Answer 1

Using the sum and product properties of roots,
sum of roots = 4+5√(5) + 4-5√(5) = 8
product of roots = (4+5√5)(4-5√5)
= 16 - 25(5) = -109

so the simplest possible quadratic is
x^2 - 8x - 109 = 0

check: https://www.wolframalpha.com/input/?i=solve+x%5E2+-+8x+-+109+%3D+0