SOLUTION: If a, b, c are in arithmetic sequence then find roots of equation: {{{ ax^2 -2bx + c = 0 }}}?

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Question 1184300: If a, b, c are in arithmetic sequence then find roots of equation:
+ax%5E2+-2bx+%2B+c+=+0+?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!



ax%5E2-2bx%2Bc=0+
Since a, b and c are in AP
=> 2b=a%2Bc
Given, quadratic equation,
ax%5E2-2bx%2Bc=0+
ax%5E2-%28a%2Bc%29x%2Bc=0 .................substitute 2b=a%2Bc+
+ax%5E2-ax-cx%2Bc=0
%28ax%5E2-ax%29-%28cx-c%29=0
+ax%28x-1%29-c%28x-1%29=0
%28x-1%29%28ax-c%29=0
roots:
x=1, or x=c%2Fa

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