Answer
$a=1$
$b=-2$
$c=-1$
Work Step by Step
Given:
$ax^{2} + bx + c$
$x=1+\sqrt 2$
$x=1-\sqrt 2$
Use the reverse zero factor property and equate the solns $1+\sqrt 2$ and $1-\sqrt 2$ by 0
$x=1+\sqrt 2$
$x-1-\sqrt 2=0$
$x=1-\sqrt 2$
$x-1+\sqrt 2=0$
Multiply the 2 equations to find the quadratic equation of the solutions
$(x+(-1+\sqrt 2))(x+(-1+\sqrt 2))=0$
$x^{2}-2x-1=0$
Notice the similarities of the quadratic equation and identify the values of a, b, and c by just observing the values
$ax^{2} + bx + c$
$x^{2}-2x-1=0$
$a=1$
$b=-2$
$c=-1$
