Question

5x^2-4x-3=0 by formula methof

Answer 1

Answer:

Step-by-step explanation:

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     5

                     B   =    -4

                     C   =   -3

Accordingly,  B2  -  4AC   =

                    16 - (-60) =

                    76

Applying the quadratic formula :

              4 ± √ 76

  x  =    —————

                   10

Can  √ 76 be simplified ?

Yes!   The prime factorization of  76   is

  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).

√ 76   =  √ 2•2•19   =

               ±  2 • √ 19

 √ 19   , rounded to 4 decimal digits, is   4.3589

So now we are looking at:

          x  =  ( 4 ± 2 •  4.359 ) / 10

Two real solutions:

x =(4+√76)/10=(2+√ 19 )/5= 1.272

or:

x =(4-√76)/10=(2-√ 19 )/5= -0.472

Two solutions were found :

x =(4-√76)/10=(2-√ 19 )/5= -0.472

x =(4+√76)/10=(2+√ 19 )/5= 1.272

Hope it will help you