The discussion centers on proving that if the quadratic equation ax² + bx + c = 0 holds for all x, then the coefficients must satisfy a = b = c = 0. Participants suggest substituting specific values for x, such as 0, 1, and -1, to generate a system of equations. This method effectively demonstrates that the only solution is when all coefficients are zero, confirming the proof. The approach emphasizes the utility of substituting values in polynomial equations to derive necessary conditions for coefficients.
PREREQUISITESStudents beginning their studies in linear algebra, educators teaching quadratic equations, and anyone interested in mathematical proofs and problem-solving techniques.
Welcome to Physics Forums!drestupinblac said:Q: Show that if ax^2 + bx + c = 0 for all x, then a=b=c=0
Please help, I'm just starting out in Linear Algebra and I'm not sure how to even start going about proving this. Thanks!