Rduce the equation to quadratic form, Algebra

Solve following equations.

                                        y -6 - 9 y -3 + 8 = 0

Solution

y -6 - 9 y -3 + 8 = 0

For this part notice that,

-6 = 2 (-3)

and thus we do have an equation which is reducible to quadratic form.  The substitution is,

u = y -3             u 2  = ( y -3 )2  = y -6

The equation becomes,

u 2 - 9u + 8 = 0                      

 (u - 8) (u -1) = 0                          u = 1, u = 8

Now, y's is going to take a little more work here, however shouldn't be too bad.

u =1:          ⇒  y -3 =   1/ y3 =1  ⇒ y3  =1/1=1 ⇒       y = (1)1/3  = 1

u = 8:  ⇒         y -3  =  1 /y3 = 8           ⇒ y3  = 1/8             ⇒  y = (1 /8)(1/3 ) =1/2

The two solutions to this equation are following

                         y= 1 and        y = 1/2 .

In this case we acquire four solutions & two of them are complex solutions. Getting complex solutions out of these are in fact more common that this set of instance might recommend. The problem is that to obtain some of the complex solutions need knowledge which we haven't (and won't) cover in this course. Thus, they don't show up all that often.

All of the examples to this point gave quadratic equations that were factorable or in the case of the last part of the earlier example was an equation that we could employ the square root property on.  That need not always be the case however.  This is more than possible that we would require the quadratic formula to do some of these.  We need to do an example of one of these just to make the point.

Posted Date: 4/6/2013 5:14:52 AM | Location : United States







Related Discussions:- Rduce the equation to quadratic form, Assignment Help, Ask Question on Rduce the equation to quadratic form, Get Answer, Expert's Help, Rduce the equation to quadratic form Discussions

Write discussion on Rduce the equation to quadratic form
Your posts are moderated
Related Questions
How may courts have 18000-18999 seats ? Use the graph


Activity 1: Graphing To fill an order for Sizzlin'' Sauce sauces, you bought 1050 green peppers and 1200 hot chili peppers. • Write and graph a system of inequalities to represent


Thirty percent of the students in a mathematics class received an “A.” If 18 students received an “A,” which of the following represents the number of students in the class?


can you help and is it free?

A segment of a circle has an area of 4.3 square feet, and the radius of the circle is 2 feet. Find the central angle.