Find All Real Solutions of the Quadratic Equation
Solve Equations of the Quadratic Form
This is a tutorial with on solving equations which may be written in quadratic form. Examples with detailed solutions and explanations are included.
Review
A quadratic equation has the form
with the coefficient a not equal to 0.
There are several methods to solve quadratic equations. In this tutorial we use the method of the quadratic formula and Discriminants
and the method of factoring
Examples with SolutionsExample 1Find all real solutions to the equation.Solution to Example 1:
Check Solutions
Conclusion: The real solutions to the given equation are √(2) and -√(2) Matched Exercise 1 Find all real solutions to the equation. Answer to Matched Exercise Example 2Find all real solutions to the equationSolution to Example 2:
= 5 Right Side = 5 Conclusion: Matched Exercise 2. Find all real solutions to the equation. Answer to Matched Exercise Solutions to Matched ExercisesMatched Exercise 1Find all real solutions to the equation.Let u = x 2 The above equation may be written as u 2 - 2 u - 3 = 0 Solve the above for u to obtain the solutions u = - 1 and u = 3 We now solve for x. u = x 2 = - 1 , this equation has no real solutions. u = x 2 = 3 gives x = √3 and x = - √3 The given equation has 2 real solutions. x3 = √3 x4 = - √3 Matched Exercise 2Find all real solutions to the equation.The given equation is now written in terms of u as follows u 2 - 3 u - 4 = 0 Solve the above quadratic equation for u to obtain u = - 1 and u = 4 Solve for x u = √x = - 1 , this equation has no real solution √x is positive u = √x = 4 , square both sides to obtain the solution x = 16 More References and linksSolve Equations, Systems of Equations and Inequalities. |
Find All Real Solutions of the Quadratic Equation
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