Question

Find the reminder (2ysquare-3y square+5)÷(2y-1)

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Answer 1

Answer:

(3y-5)(2y-1)=10

2 result(s) found

y=−31=−0.333

y=25=2.500

 

Note that the square root of

   (y-(13/12))2   is

   (y-(13/12))2/2 =

  (y-(13/12))1 =

   y-(13/12)

 

 According to the Quadratic Formula,  y  , the solution for   Ay2+By+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  y =   ————————

                      2A

  In our case,  A   =     6

                      B   =   -13

                      C   =   -5

Accordingly,  B2  -  4AC   =

                     169 - (-120) =

                     289

Applying the quadratic formula :

               13 ± √ 289

   y  =    ——————

                      12

Can  √ 289 be simplified ?

Yes!   The prime factorization of  289   is

   17•17 

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 289   =  √ 17•17   =

                ±  17 • √ 1   =

                ±  17

So now we are looking at:

           y  =  ( 13 ± 17) / 12

Two real solutions:

y =(13+√289)/12=(13+17)/12= 2.500

or:

y =(13-√289)/12=(13-17)/12= -0.333

Two solutions were found :

 y = -1/3 = -0.333

 y = 5/2 = 2.500