2014 · Q26
If the roots of the equation (a^2 - bc)x^2 + 2(b^2 - ac)x + (c^2 - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?
Elementary MathematicsAlgebra
- Aa + b + c = abc
- Ba^2 + b^2 + c^2 = 0
- Ca^3 + b^3 + c^3 = 0
- Da^3 + b^3 + c^3 = 3abc
Explanation
Equal roots give discriminant zero: (b^2-ac)^2 = (a^2-bc)(c^2-ab), which simplifies to a^3 + b^3 + c^3 = 3abc.