Question

5tsquare -8t-12=0 by the factorise method​

Answer 1

Step-by-step explanation:

     Solving    5t2-8t-12 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  t  ,the solution for   At2+Bt+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  t =   ————————

                      2A 

  In our case,  A   =     5

                      B   =    -8

                      C   =  -12 

Accordingly,  B2  -  4AC   =

                     64 - (-240) =

                     304

Applying the quadratic formula :

               8 ± √ 304 

   t  =    —————

                    10

Can  √ 304 be simplified ?

Yes!   The prime factorization of  304   is

   2•2•2•2•19  

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).

√ 304   =  √ 2•2•2•2•19   =2•2•√ 19   =

                ±  4 • √ 19 

  √ 19   , rounded to 4 decimal digits, is  4.3589

 So now we are looking at:

           t  =  ( 8 ± 4 •  4.359 ) / 10

Two real solutions:

 t =(8+√304)/10=(4+2√ 19 )/5= 2.544 

or:

 t =(8-√304)/10=(4-2√ 19 )/5= -0.944 

Two solutions were found :

 t =(8-√304)/10=(4-2√ 19 )/5= -0.944

 t =(8+√304)/10=(4+2√ 19 )/5= 2.544