Question

verify that the numbers 1+ sqrt 5 and 1- sqrt5 both satisfy the equation x^2-2x-4=0

Answer 1

\[s=x1+x2 =(1-\sqrt{5})+(1+\sqrt{5})=2\\p=x1*x2 =(1-\sqrt{5})*(1+\sqrt{5})=-4\\x^2-sx+p\]

Answer 2

so it doesn't satisfy it?

Answer 3

put these values in the equation

Answer 4

or wait i have a better method make the quadratic using the roots given and compare it with the quadratic equation given

Answer 5

\[x^2-(1+\sqrt5+1-\sqrt5)x+(1-\sqrt5)(1+\sqrt 5)=0\]

Answer 6

\[x^2-2x-4=0\]

Answer 7

okay makes sense thanks