Help with simple linear algebra/quadratic equation proof

[drestupinblac]

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!

 

[Mark44]

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!

Welcome to Physics Forums!

If ax^2 + bx + c = 0 for all x, it's certainly true for, say, x = 0, x = 1, and x = -1. Substitute those values in your equation to get three equations in three unknowns, and solve for the three unknowns.

 

[drestupinblac]

Thank you for the warm welcome :) The answer seems almost obvious now that I see it, I guess I didn't think it would be as easy as choosing values for x.