THREE
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
With considerable difficulty since there are a lot more than 3 possible outcomes.
The discriminant is -7
The discriminant is 16
If the discriminant of a quadratic equation is zero then it has equal roots. If the discriminant is greater than zero then there are two different roots. If the discriminant is less than zero then there are no real roots.
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.
It can tell you three things about the quadratic equation:- 1. That the equation has 2 equal roots when the discriminant is equal to zero. 2. That the equation has 2 distinctive roots when the discriminant is greater than zero. £. That the equation has no real roots when the discriminant is less than zero.
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
There are 23 = 8 possible outcomes.
THREE
There are two outcomes for each coin and three coins; 2 x 2 x 2 = 23 = 8 outcomes.
With the standard notation, If b2 < 4ac then the discriminant is negative If b2 = 4ac then the discriminant is zero If b2 > 4ac then the discriminant is positive
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
With considerable difficulty since there are a lot more than 3 possible outcomes.
18 outcomes
12