<PRE><B>Question 175025</B>
Find the missing root and solve for k:
 2x^2 - 12x + k = 0; 
r1 = 3 + {{{sqrt(2)}}}
r2 = 3 - {{{sqrt(2)}}}
:
Find k:
x = 3 + {{{sqrt(2)}}}
x - 3 = {{{sqrt(2)}}}
square both sides
(x-3)^2 = ({{{sqrt(2)}}})^2
:
x^2 - 6x + 9 = 2
:
x^2 - 6x + 9 - 2 = 0
:
x^2 - 6x + 7 = 0
:
I left a step out here
2(x^2 - 6x + 7) = 2x - 12x + 14; the original equation
therefore
k = 14
:
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