SOLUTION: Find the missing root and solve for k: 2x^2 - 12x + k = 0; r1 = 3 + square root of 2

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Question 175025:
Find the missing root and solve for k: 2x^2 - 12x + k = 0; r1 = 3 + square root of 2
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the missing root and solve for k:
2x^2 - 12x + k = 0;
r1 = 3 + sqrt%282%29
r2 = 3 - sqrt%282%29
:
Find k:
x = 3 + sqrt%282%29
x - 3 = sqrt%282%29
square both sides
(x-3)^2 = (sqrt%282%29)^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
:

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%5E2+-+12x+%2B+k+=+0
x%5E2+-+6x+%2B+k%2F2+=+0
given:
r%5B1%5D+=+3+%2B+sqrt%282%29
%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+=+0
x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29%2Ax+%2B+r%5B1%5Dr%5B2%5D+=+0
-6+=+-%283+%2B+sqrt%282%29+%2B+r%5B2%5D%29
r%5B2%5D+=+3+-+sqrt%282%29 the missing root
------------------------
k%2F2+=+r%5B1%5Dr%5B2%5D
k+=+2%2A%283+%2B+sqrt%282%29%29%2Ar%5B2%5D
k+=+2%2A%283+%2B+sqrt%282%29%29%283+-+sqrt%282%29%29
k+=+2%2A%289+-+2%29
k+=+14
The equation is
+2x%5E2+-+12x+%2B+14+=+0
check:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+-12
c+=+14
x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A2%2A14+%29%29%2F%282%2A2%29+
x+=+%28+12+%2B-+sqrt%28+144+-+112+%29%29%2F4+
x+=+%28+12+%2B-+sqrt%28+32+%29%29%2F4+
x+=+%283+%2B+sqrt%282%29%29
x+=+%283+-+sqrt%282%29%29
OK