If a quadratic equation ax^2+bx+c=0. is satisfied by more than two distinct complex numbers then it becomes an identity i.e a=b=c=0...explain this

Question

If a quadratic  equation ax^2+bx+c=0. is satisfied by more than two distinct complex numbers then it becomes an identity i.e a=b=c=0...explain this

anonymous · Answer

@igbasallote

anonymous · Answer

if suppose the equation has more than 2 roots , then it should cut the x-axis more than 2 times.But a parabola cannot cut the x axis more than twice.so a=0.now  even bx+c can cut x axis more than twice only when b=0,c=0

anonymous · Answer

I'm impressed.  I was thinking that a quadratic can have 2 roots at the most, so I didn't understand the question.  But the identity is 0=0.  I love your reasoning.  That can only happen one way.  Somehow, you came up with a geometric interpretation... that's awesome.  Now I'm wondering... what would the roots be?

anonymous · Answer

@ash2007ray when b=c=0 the point is in the origin and how did you say that it cuts x axis twice..I dint understand..help please.

hartnn · Answer

ok,y=bx+c is equation of straight line
when b=c=0,u have y=0,which is entire x-axis
so y=bx+c intersects/cuts x axis at infinite(>2) points

anonymous · Answer

Thanks man...but can a quadratic equation have more than two solutions and how is this possible..actually I read this question in a book

hartnn · Answer

first of all,since a is 0,that equation is not a quadratic equation at all!!
because the defination of quadratic eq mentions the condition,a not=0
it is because of this condition that we say that it has only 2 solutions....
if u don't use a not=0,then u can have many or infinite solutions....and contradictions to fact that quadratic equation have only two solutions