How do you know if a quadratic equation will have one, two, or no solutions?

Answer by  esteban (1334)

First, put the equation in standard form: ax^2 + bx + c = 0, where a, b, and c are the coefficients. Then evaluate the expression b^2 - 4ac. If b^2 - 4ac is positive, there are 2 solutions. If b^2 - 4ac is negative, there are no solutions. If b^2 - 4ac is 0, there is 1 solution.

Answer by  bandi (39)

if the rank of the augmented matrix[AB]=rank of A=2, then it has two solutions if the rank of the augmented matrix[AB]=rank of A<2, then it has one solution if the rank of the augmented matrix[AB] not equal to rank of A, then it has no solution