Question

Write the absolute value equation if it has the following solutions.

Answer 1

The absolute value equation is $x^{2} +x-8.75=0$, if the solutions are x=2.5 and x=-3.5.

Step-by-step explanation:

The given is,

                Two solutions: x = 2.5 and x = -3.5

Step:1

               In this question we use reverse method of quadratic equation solve method,

               From first solution, x = 2.5

                                       x - 2.5 = 0..........................(1)

               From the second solution, x = -3.5

                                               x + 3.5 = 0.................(2)

                From the equations (1) and (2),

                          ( x - 2,5 ) ( x + 3.5 )  = 0

               Multiply the equations,

                   $(x^{2} +3.5x-2.5x-8.75)=0$

                                     $x^{2} +x -8.75=0$

Step:2

            Check for solution,

                              $x^{2} +x -8.75=0$..........................(3)

            Substitute the value of x=2.5 in above equation,

                          $2.5^{2} +2.5 -8.75=0$

                         6.25 + 2.5 - 8.75 = 0

                                                 0 = 0          

Result:

           The absolute value equation is $x^{2} +x-8.75=0$, if the solutions are x=2.5 and x=-3.5.