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## Finding and Using the Discriminant

#### High School - HSA-REI.B.4b

What Is a Discriminant? (In Math) Remember the quadratic formula? For any quadratic equation like; ax2 + bx + c =0 Here, we are discussing a part of the quadratic formula- the discriminant. THE DISCRIMINANT - The discriminant is that of a quadratic formula that is present under the square root, which is b2 - 4ac. The discriminant can be a positive number, a negative number, or a zero. It determines the number of possible solutions to the given quadratic equation - A positive discriminant shows that a quadratic equation has two distinct real number solutions. - A negative discriminant shows that neither of the two solutions is a real number. - A zero discriminant shows that a quadratic equation has repeated a real number solution. EXAMPLE - Suppose, you are asked to find out how many solutions the following quadratic equation has, 2x2 + 5x - 1 = 0 From the above equation, we get: a= 2, b= 5, c= -1 putting these values in the discriminant, we get: b2 – 4ac, (5)2 – 4(2)(-1), 25 - (-8), 25 + 8 = 33, 33 is a positive number, so it means that the quadratic has two solutions.

### Printable Worksheets And Lessons  #### Homework Sheets

This skill use to just apply to trigonometry, but we see it pop up with algebra more often now.

• Homework 1 - Find the value of the discriminant by breaking down what appears under the radical.
• Homework 2 - The discriminant of a quadratic equation (ax^2 + bx +c = 0) is b^2 - 4ac. It is the expression under the radial in the quadratic formula.
• Homework 3 - Four problems that are totally broken down for you.

#### Practice Worksheets

• Practice 1 - Apply the formula and run away with it. There is plenty of space to work with here.
• Practice 2 - How many moves can you do it in?
• Practice 3 - The discriminant can also tell you the nature of the possible solutions.

#### Math Skill Quizzes

See if you can spot the pattern I have going on in these.

• Quiz 1 - When a discriminant has a positive value there are two solutions and the as a result two x-intercepts.
• Quiz 2 - When it is zero, there is only one solution and one x-intercept.
• Quiz 3 - When it is negative there are no solutions and no x-intercepts.

### Why is This Value Important to Us?

The nature of this value is important for us to understand the different possible and types of solutions when working with quadratic equations. This is a great way to check your final answer. When working with these problems we can solve them in one of four different ways. Factoring can be used to condense and expand problem sets. We can use the complete the square method when we are dealing with complicated equations. We can also use the square root method to collect all the exponentials and place them to one side of the equation. If the quadratic is in standard form, we can simply use the quadratic formula to solve it. Which method we use to process these calculations is all dictated by understanding the spirit of the discriminant.