## Algebra

Showing posts with label solutions. Show all posts
Showing posts with label solutions. Show all posts

If a quadratic equation factors then certainly you should solve it by factoring. The problem is that not all quadratic equations factor. When this is the case we could use the quadratic formula to find the solutions. (We will limit our introduction to equations where b^2 - 4ac >= 0 .)

Most textbooks provide a nice proof of the quadratic formula. The proof involves solving the general quadratic by completing the square. This study guide will focus on using the formula to solve problems.

Step 1: Identify the coefficients a, b, and c.
Step 2: Write down the formula (you should memorize it).
Step 3: Substitute in the appropriate values and then evaluate.

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### Solving Equations Quadratic in Form

In this section, we make use of all the techniques that we have learned so far for solving quadratic equations. In fact, the equations found here are reducible to quadratic form.

Here are most of the reducible equations that we are likely to encounter. Begin by trying to identify what can be squared to obtain the leading variable term.
Tip: Look at the middle term for a hint as to what u should be.
In the previous solved problem, we certainly could have distributed the expression on the left side, put the equation in standard form then re-factored it. Instead, here we are illustrating a technique that will be used to easily solve many other equations that are quadratic in form.

Solve by making a u-substitution.

Solve: x^6 + 26x^3 -27

Six Answers: { -3, 1, (3±3iSqrt(3))/2, (-1±iSqrt(3))/2 }

So far we have been able to factor after we make the u-substitution.  If the resulting quadratic equation does not factor, then use the quadratic formula.