SOLUTION: one root of the equation 2x2-x+c=0 is double the other root. find c

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Question 1005804: one root of the equation 2x2-x+c=0 is double the other root. find c
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2-x%2Bc=0
If you want only ONE repeated root, then discriminant must be 0.

%28-1%29%5E2-4%2A2%2Ac=0
1-8c=0
8c=1
highlight%28c=1%2F8%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
one root of the equation 2x%5E2-x%2Bc=0 is double the other root
find c+

let one root be alpha
then the other root will be 2alpha
recall that sum of roots: -b%2Fa
so, alpha%2B2alpha=-b%2Fa
3alpha=+-b%2Fa....since in 2x%5E2-x%2Bc=0, a=2and b=-1 we have 3alpha=+-%28-1%29%2F2
3alpha=+1%2F2
alpha=+1%2F%282%2A3%29
alpha=+1%2F6.........one root
2alpha=+2%2F6=1%2F3....the other root
recall that product of roots: c%2Fa
alpha%2A2alpha=+c%2Fa
2%28alpha%29%5E2=+c%2F2
%28alpha%29%5E2=+c%2F4 substitute 1%2F6 for alpha
%281%2F6%29%5E2=+c%2F4
%281%2F36%29=+c%2F4
4%281%2F36%29=+c
cross%284%29%281%2Fcross%2836%299%29=+c
c=1%2F9
your equation is:
2x%5E2-x%2B1%2F9=0