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.

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