Answer:
[tex]x^2-x-1=0[/tex]
Step-by-step explanation:
Let [tex]x_1[/tex] and [tex]x_2[/tex] be the roots of the required quadratic equation.
Then the equation is formed using:
[tex]x^2-(sum\:of\:roots)x+product\:of\:roots=0[/tex]
or
[tex]x^2-(x_1+x_2)x+x_1*x_2=0[/tex]
From the given information, sum of the roots is:
[tex]x_1+x_2=1[/tex] and the product is
[tex]x_1x_2=-1[/tex]
Therefore the required equation is
[tex]x^2-x-1=0[/tex]
