Question

a quadratic equation of the form x^2+kx+m=0 has solutions x=3+2√2 and x=3-2√2. what is the value of k+m?

Answer 1

if you have equation ax^2+bx+c, then according to Vieta's formula, if x1 and x2 are roots of equation, then x1+x2=-(b/a) and x1*x2=c/a

Answer 2

yep, follow this method ^^

Answer 3

=0, btw

Answer 4

\[(x-(3+2\sqrt{2})(x-(3-2\sqrt{2}))\]
\[m=(3+\sqrt{2})(3-2\sqrt{2})\]
\[k=-(3+2\sqrt{2})-(3-2\sqrt{2})\]

Answer 5

so all i have to do is add x1+x2?

Answer 6

mathmagician wrote a better more general answer. you can see why it is true by writing the quadratic in factored form and multiplying out