Answer:
[tex]b=-6\\c=7[/tex]
Step-by-step explanation:
we know that
The general equation of a quadratic function in factored form is equal to
[tex]y=a(x-x_1)(x-x_2)[/tex]
where
a is a coefficient of the leading term
x_1 and x_2 are the roots
we have
[tex]a=1\\x_1=3+\sqrt{2}\\x_2=3-\sqrt{2}[/tex]
substitute
[tex]y=(1)(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))[/tex]
Applying the distributive property convert to expanded form
[tex]y=x^2-x(3-\sqrt{2})-x(3+\sqrt{2})+(3+\sqrt{2})(3-\sqrt{2})[/tex]
[tex]y=x^2-(3x-x\sqrt{2})-(3x+x\sqrt{2})+(9-2)[/tex]
[tex]y=x^2-3x+x\sqrt{2}-3x-x\sqrt{2}+7[/tex]
[tex]y=x^2-6x+7[/tex]
therefore
[tex]b=-6\\c=7[/tex]
