Week 7 – Pre Calc 11

This week in Pre-Calculus 11 we finished the solving quadratic equations unit. This week we learned about the discriminant of a quadratic equation. The discriminant can be very helpful when solving a quadratic equation because it helps determine how many solutions the equation has.

What is the Discriminant? The discriminant is from the quadratic formula. The discriminant can be calculated by using . Depending on whether the discriminant of a quadratic equation is positive, negative or zero you can determine how many solutions the equation may have. If the discriminant is a positive number the equation will have two solutions, if the discriminant is negative there will be no solutions, and if the discriminant is equal to zero then the equation will have one solution.

Ex.

a= 4

b= 3

c= -15

 

265 

The example above will have 2 solutions because the discriminant is positive.

Ex.  

a= 1

b= 5

c= 7

 

 

-3 

The example above will have 0 solutions because the discriminant is negative. The discriminant is the radicand of the quadratic formula and because there cannot be negatives in the radicand there will be no solution.

Ex.

a= 9

b= 6

c= 1

 

0 

The example above will have one solution because the discriminant is equal to zero. Before solving for the discriminant you can simplify the equation by taking out a common factor from all of the terms.

 

 

a= 1

b= 3

c= -4 

 

25

The discriminant above is positive which means that there will be two solutions to the equation.