# Problem Solving With Quadratic Equations

Note that the second value could have been gotten by changing the sign on the extraneous solution.

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This gave us an equivalent equation—without fractions—to solve.

We can use the same strategy with quadratic equations. We know from the Zero Products Principle that this equation has only one solution: .

But the Quadratic Formula took longer and provided me with more opportunities to make mistakes.

Warning: Don't get stuck in the rut of always using the Quadratic Formula!

That can happen, too, when using the Quadratic Formula.

If we get a radical as a solution, the final answer must have the radical in its simplified form.To use the Quadratic Formula, we substitute the values of into the expression on the right side of the formula.Then, we do all the math to simplify the expression.This quantity is called the When the discriminant is positive the quadratic equation has two solutions.When the discriminant is zero the quadratic equation has one solution.’ The answer is ‘yes.’ In this section, we will derive and use a formula to find the solution of a quadratic equation.We have already seen how to solve a formula for a specific variable ‘in general’ so that we would do the algebraic steps only once and then use the new formula to find the value of the specific variable.When the discriminant is negative the quadratic equation has no real solutions. Most people find that method cumbersome and prefer not to use it.We needed to include it in this chapter because we completed the square in general to derive the Quadratic Formula. She wants to have a triangular window looking out to an atrium, with the width of the window 6 feet more than the height.Since I'll be cutting equal-sized squares out of all of the corners, and since the box will have a square bottom, I know I'll be starting with a square piece of cardboard.In this last exercise above, you should notice that each solution method gave the same final answer for the cardboard's width.

## Comments Problem Solving With Quadratic Equations

• ###### General Quadratic Word Problems - Purplemath Home
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Most quadratic word problems should seem very familiar, as they are built from the linear problems that you've done in the past. A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?…

• ###### Ways to Solve Quadratic Equations - wikiHow
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A quadratic equation is a polynomial equation in a single variable where the highest exponent of the variable is 2. There are three main ways to solve quadratic equations 1 to factor the quadratic equation if you can do so, 2 to use the quadratic formula, or 3 to complete the square.…

• ###### Solve quadratic equations with the quadratic formula.
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Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14. If you're seeing this message, it means we're having trouble loading.…

• ###### Quadratic Equations Solved Problems and Practice Questions.
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In this article we cover quadratic equations – definitions, formats, solved problems and sample questions for practice. A quadratic equation is a polynomial whose highest power is the square of a variable x 2, y 2 etc. A polynomial that contains two terms is called a binomial expression. A.…

• ###### Solving quadratic equations by factoring examples
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Here we are going to see some example problems on solving quadratic equations using the method factoring. Solving quadratic equations by factoring in the form ax ² + bx + c. Whenever we have a quadratic equation in the form ax ² + bx + c and we need to factor this, first we have to check whether the coefficient of x ² is 1 or not.…

• ###### Word problems involving quadratic Equations with solutions.
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In order to learn how to solve quadratic equations by four different methods, please follow this tutorial. This tutorial assumes that you have already got a good skill in solving quadratic equations as explained in the above tutorial. This tutorial primarily focuses on solving real-world problems involving quadratic equations. E.g.1…

• ###### Quadratic Equations - Problems 1
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Quadratic Functions Problems with Solutions Parabola Questions and Problems with Detailed Solutions Solve Quadratic Equations Using Discriminants Solve Equations, Systems of Equations and Inequalities.…

• ###### Real World Examples of Quadratic Equations - Math is Fun
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Quadratic Equations are useful in many other areas For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation. Quadratic equations are also needed when studying lenses and curved mirrors. And many questions involving time, distance and speed need quadratic equations.…

• ###### Algebra - Quadratic Equations - Part I Practice Problems
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Here is a set of practice problems to accompany the Quadratic Equations - Part I section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.…