Rduce the equation to quadratic form, Algebra

Solve following equations.

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


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
what is the equivalent exponential of log3 5=y

The process for finding the inverse of a function is a quite simple one although there are a couple of steps which can on occasion be somewhat messy.  Following is the process G

one no. is 7 more than another and its square is 77 more than the square of the smaller number.What are the numbers?

I have a homework question to use the factor theorem that I need to use Synthetic Substitution with. I did all the work and the divisor is a factor but the equation I have to use t

How do you write 14x14x14x14x14x14x14= in exponential form?

Example :   Use the quadratic formula to solve following equation.                            x 2 + 2x = 7 Solution Here the important part is to ensure that before we b