Question

state the discriminant of the quadratic formula and describe for which values of the discriminant a quadratic equation will have real solutions, for which values it will have imaginary solutions, and for which values it will have one solution

Answer 1

The discriminant is the part of the quadratic formula

The discriminant tells us whether there are two solutions, one solution, or no solutions .

Discriminant ( D ) = b^2 - 4*a*c

1 ) The discriminant of the quadratic equation will have real solution when

  Discriminant > 0

D > 0

b^2 - 4*a*c > 0

A positive discriminant indicates that the quadratic equation has two distinct real number solutions.

2 ) The discriminant of the quadratic equation will have imaginary solution when

Discriminant < 0

D < 0

b^2 - 4*a*c < 0

A negative discriminant indicates that neither of the solutions are real numbers.

3 ) The discriminant of the quadratic equation will have one solution when

  Discriminant = 0

D = 0

b^2 - 4*a*c = 0

A discriminant of zero indicates that the quadratic equation has a repeated real number solution.

Both the solutions are repeated so it is considered only one solution