That its roots (solutions) are coincident.
That its roots (solutions) are coincident.
If the discriminant of a quadratic equation is less than zero then it has no solutions.
The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative
That the discriminant of the quadratic equation must be greater or equal to zero for it to have solutions. If the discriminant is less than zero then the quadratic equation will have no solutions.
Yes and they will be of equal value
If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.
It will then have two equal real solutions
If the discriminant of the quadratic equation is equal or greater than zero it will have 2 solutions if it is less than zero then there are no solutions.
As stated in the attached link, there are three possible discriminant conditions: Positive, Zero, or Negative. If the discriminant is negative, there are no real solutions but there are two imaginary solutions. So, yes there are solutions if the discriminant is negative. The solutions are imaginary, which is perfectly acceptable as solutions.
There are no solutions because the discriminant of this quadratic equation is less than zero
That depends on the values of the polynomial but in general:- If the discriminant is greater than zero it has 2 solutions If the discriminant is equal to zero then it has 2 equal solutions If the discriminant is less than zero it has no solutions