Predicting the Type of Solutions Using the Discriminant (2.5.3)

Question 1

• The discriminant is the quantity under the radical in the quadratic formula.

Answer 1

• The discriminant is the quantity under the radical in the quadratic formula.

Question 2

• The discriminant for the equation ax^2+ bx + c = 0, is b^2 – 4ac.

Answer 2

• The discriminant for the equation ax^2+ bx + c = 0, is b^2 – 4ac.

Question 3

• The discriminant is important because we can analyze it to determine in advance the number and nature of the solutions of the quadratic equation in question.
• If the discriminant = 0, there is only one real solution to the equation.
• If the discriminant is positive, there are two real solutions.
• If the discriminant is negative, there are two complex solutions.

Answer 3

• The discriminant is important because we can analyze it to determine in advance the number and nature of the solutions of the quadratic equation in question.
• If the discriminant = 0, there is only one real solution to the equation.
• If the discriminant is positive, there are two real solutions.
• If the discriminant is negative, there are two complex solutions.

Question 4

• Evaluating the discriminant is very useful, BUT it does NOT give you the answers, just information about the answers.

Answer 4

• Evaluating the discriminant is very useful, BUT it does NOT give you the answers, just information about the answers.

Question 5

Doing this analysis is a simple matter:

1. Substitute your a, b, and c values
   into the discriminant.
2. Do the arithmetic to see if the quantity
   is 0, > 0, or

Answer 5

Doing this analysis is a simple matter:

1. Substitute your a, b, and c values
   into the discriminant.
2. Do the arithmetic to see if the quantity
   is 0, > 0, or