SOLUTION: Find k so that the roots of (2k-1)x^2 + (k-1)x - 16 = 0 are numerically equal but opposite in sign.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find k so that the roots of (2k-1)x^2 + (k-1)x - 16 = 0 are numerically equal but opposite in sign.      Log On


   

Question 1094972: Find k so that the roots of (2k-1)x^2 + (k-1)x - 16 = 0 are numerically equal but opposite in sign.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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If "the roots are numerically equal but opposite in sign", it means that the sum of roots is ZERO.


From the other side, according to Vieta's theorem, the sum of the roots of the quadratic polynomial is equal to its coefficient at "x", 
taken with the opposite sign and divided by the leading coefficient.


It means that the coefficient at "x" must be equal to ZERO.


Hence, k = 1.


Answer.  The necessary and sufficient condition is k = 1.

Solved.