Question

One root of 3x^2-kx+69=0 is 5+sqrt(2). What is the value of k?

Answer 1

by the irrational root theorem, if 5+sqrt(2) is a root, then its conjugate is a root as well.

(x-(5+sqrt(2))(x-(5-sqrt(2))

Answer 2

However the answer isnt the conugate

Answer 3

of course -- im just giving some information that will help you find the answer

Answer 4

oh :P

Answer 5

so, if we found the equivalent expression with those roots by distributing...
(x-(5+sqrt(2))(x-(5-sqrt(2))
x^2 - (5+sqrt(2))x - (5-sqrt(2))x + (5+sqrt(2))(5-sqrt(2))
x^2 - 5x + sqrt(2)x - 5x + sqrt(2)x + 5^2 - sqrt(2)^2
x^2 - 10x + 25 - 2
x^2 - 10x + 23

x^2 - 10x + 23 should be equal to 3x^2 - kx + 63