Need math help with problem

Question

I need help with a math problem,

For a given polynomial, a given zero is 2 + 5√3, what would be another zero?

Ive tried to solve it myself but can’t think of any ways to do it. If anyone could help, I’d appreciate it :)

Answer 1

the other zero is 2-5sqr3 the 2 zeroes are a conjugate pair

x^2 -4x -71=0, complete the square

x^2-4x + 4 = 71+4 = 75

(x-2)^2 =75 take square roots of both sides

x-2 + = + or - sqr75 = - or + 5sqr3

x = 2 + or - 5sqr3 = 2+5sqr3, 2-5sqr3

the zeroes or roots are 2+5sqr3 and 2-5sqr3