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

We will begin with inequalities that only have a single inequality in them.  The thing that we've got to keep in mind here is that we're asking to find out all the values of the

what are the two types of ogive curves

Estimate the values to the nearest hundredth and show your work 40

Have a % 56% discount have the amount of 285.13 what was the amount used to get to 285.13? How did you get?

This is my question I need help with: The ratio of adult dogs to puppies at a park on Monday was 3:2. There are 12 puppies there that day. Tuesday, 15 adult dogs were at the park.

I need examples for a tutorial I have do in my AVID class.

30. 5x-1 greater than 29