Home Systems of Equations Adding and Subtracting Rational Expressions with Different Denominators Graphing Linear Equations Raising an Exponential Expression to a Power Horizontal Line Test Quadratic Equations Mixed Numbers and Improper Fractions Solving Quadratic Equations by Completing the Square Solving Exponential Equations Adding and Subtracting Polynomials Factorizing simple expressions Identifying Prime and Composite Numbers Solving Linear Systems of Equations by Graphing Complex Conjugates Graphing Compound Inequalities Simplified Form of a Square Root Solving Quadratic Equations Using the Square Root Property Multiplication Property of Radicals Determining if a Function has an Inverse Scientific Notation Degree of a Polynomial Factoring Polynomials by Grouping Solving Linear Systems of Equations Exponential Functions Factoring Trinomials by Grouping The Slope of a Line Simplifying Complex Fractions That Contain Addition or Subtraction Solving Absolute Value Equations Solving Right Triangles Solving Rational Inequalities with a Sign Graph Domain and Range of a Function Multiplying Polynomials Slope of a Line Inequalities Multiplying Rational Expressions Percent of Change Equations Involving Fractions or Decimals Simplifying Expressions Containing only Monomials Solving Inequalities Quadratic Equations with Imaginary Solutions Reducing Fractions to Lowest Terms Prime and Composite Numbers Dividing with Exponents Dividing Rational Expressions Equivalent Fractions Graphing Quadratic Functions Polynomials Linear Equations and Inequalities in One Variable Notes on the Difference of 2 Squares Solving Absolute Value Inequalities Solving Quadratic Equations Factoring Polynomials Completely Using Slopes to Graph Lines Fractions, Decimals and Percents Solving Systems of Equations by Substitution Quotient Rule for Radicals Prime Polynomials Solving Nonlinear Equations by Substitution Simplifying Radical Expressions Containing One Term Factoring a Sum or Difference of Two Cubes Finding the Least Common Denominator of Rational Expressions Conjugates Multiplying Rational Expressions Expansion of a Product of Binomials Solving Equations Exponential Growth Factoring by Grouping Solving One-Step Equations Using Models Solving Quadratic Equations by Factoring Adding and Subtracting Polynomials Rationalizing the Denominator Rounding Off The Distributive Property What is a Quadratic Equation Laws of Exponents and Multiplying Monomials The Slope of a Line Factoring Trinomials by Grouping Multiplying and Dividing Rational Expressions Solving Linear Inequalities Multiplication Property of Exponents Multiplying and Dividing Fractions 3 Formulas Dividing Monomials Multiplying Polynomials Adding and Subtracting Functions Dividing Polynomials Absolute Value and Distance Multiplication and Division with Mixed Numbers Factoring a Polynomial by Finding the GCF Roots Adding and Subtracting Polynomials The Rectangular Coordinate System Polar Form of a Complex Number Exponents and Order of Operations Graphing Horizontal and Vertical Lines Invariants Under Rotation The Addition Method Solving Linear Inequalities in One Variable The Pythagorean Theorem

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

## Using the Discriminant to predict the roots of a quadratic equation

Remember the quadratic formula for an equation in the form ax + bx + c = 0 is:

From this formula the discriminant is: b - 4ac

When you evaluate the discriminant for a quadratic equation, if the result is:

 positive You will have 2 different real solutions to the equation If this number is a perfect square number, there will be 2 different rational answers. If this number is a not perfect square number, there will be 2 different irrational answers. zero You will have 1 real, rational solution to the equation - that is, there will be a repeated answer negative You will have no real solutions to the equation (only imaginary answers)

Examples:

Use the discriminant to predict the roots of the following equations:

 1. x + 7x + 12 = 0 a = 1 b = 7 c = 12 b - 4ac = 7 - 4(1)(12) = 49 - 48 = 1

Since the result is positive, there should be 2 different real solutions.

In fact, there will be 2 different rational solutions because 1 is a perfect square number.

(Perfect square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, etc)

 2. x + 7x + 3 = 0 a = 1 b = 7 c = 3 b - 4ac = 7 - 4(1)(3) = 49 - 12 = 37

Since the result is positive, there should be 2 different real solutions.

In fact, there will be 2 different irrational solutions because 37 is not a perfect square number.

 3. x + 4x + 4 = 0 a = 1 b = 4 c = 4 b - 4ac = 4 - 4(1)(4) = 16 - 16 = 0

Since the result is zero, there should be only one real, rational solution

 4. x - x + 4 = 0 a = 1 b = -1 c = 4 b - 4ac = (-1) - 4(1)(4) = 1 - 16 = -15

Since the result is negative, there should be no real solutions.