Answer:
D is correct. [tex]x^2-2x-4=0[/tex]
Step-by-step explanation:
We are given the root of the equation
[tex]x=1+\pm \sqrt{5}[/tex]
If we are given solution of the equation then find equation using formula.
If a and b are the solution of equation then equation would be (x-a)(x-b)=0
Here, [tex] a=1+\sqrt{5} , b=1-\sqrt{5}[/tex]
Equation form would be [tex] (x-1-\sqrt{5})(x-1+\sqrt{5})=0[/tex]
Now we simplify the above equation to get correct option.
[tex] x^2-x+x\sqrt{5}-x+1-\sqrt{5}-x\sqrt{5}+\sqrt{5}-5=0[/tex]
[tex]x^2-2x-4=0[/tex]
So, D is correct. [tex]x^2-2x-4=0[/tex]
