SOLUTION: One root of the equation ax^2 + 2bx + c = 0 is the reciprocal of the square of the other root. Show that a^3 +c^3 +2abc=0.

Question 1144876: One root of the equation ax^2 + 2bx + c = 0 is the reciprocal of the square of the other root. Show that a^3 +c^3 +2abc=0.
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

 

Let r be one root.  Then the other root is 1/r²

We know that the constant term of a quadratic divided by the leading
coefficient equals the product of the roots.

So the product of the two roots is c/a, therefore









So a/c is a root and must satisfy the original equation:











Edwin

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