Question

Write the absolute value equation if it has the following solutions. Hint: Your equation should be written as x−b =c. (Here b and c are some numbers.) a Two solutions: x=2, x=13.
PLEASE HELP

Answer 1

The absolute value equation is $x^{2} -15x+26 =0$, if the equation has a two solutions of x=2 and x=13.

Step-by-step explanation:

The given is,

        Two solutions

                  x = 2

                  x = 13

Step:1

       We form the equation by the reverse method of Quadratic equation solve method,

        For first solution,

                                  x = 2

                            x - 2 = 0..............................(1)

        For second solution.    

                                 x = 13

                          x - 13 = 0..............................(2)

       From the equations (1) and (2)

                         ( x - 2 ) ( x - 13 ) = 0

      Multiply the equations,

                   $x^{2} -15x-2x+26=0$

                           $x^{2} -15x+26=0$

Step:2

       Check for solution,

                           $x^{2} -15x+26=0$

       Substitute the x value,

                         $2^{2} -15(2)+26=0$

                               $4 - 30 +26=0$

                                  $-26+26 = 0$

                                              0 = 0

Result:

          The absolute value equation is $x^{2} -15x+26 =0$, if the equation has a two solutions of x=2 and x=13.