Quadratic equations, which are expressed in the form of ax^2+bx+c=0, where a does not equal 0, may have how many solutions…explain

Question

Quadratic equations, which are expressed in the form of ax^2+bx+c=0,  where a does not equal 0, may have how many solutions…explain

pooja195 · Answer

http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.444397.html

campbell_st · Answer

well if a is not equal to zero means that the quadratic will have up to 2 solutions...


here are some examples

$$x^2 - 6x + 9 = 0.... is....(x - 3)^2 = 0 $$

has a repeated solution x = 3 or a solution with multiplicity 2

$$x^2 + x - 6 = 0.... is .... (x -2)(x+3) = 0$$

has 2  unequal solutions x = 2 and x = -3


$$x^2 + x + 2 = 0$$  has no real number solutions.... as the quadratic has complex number solutions.