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the product of two consecutive positive integers is 42. write and solve a quadratic equation to find the solutions. then show how you use those solutions to find the two consecutive positive integers.

-7 is not positive

The numbers are 6 an 7.

Step-by-step explanation:

1. Set up the equation

        Let x = the first integer. Then

         x + 1 = the next integer

     x(x + 1) = the product of the integers

     x(x + 1) = 42

       x² + x = 42     Distributed the x

x² + x - 42 = 0

2. Solve for x

(x + 7)(x - 6) = 0            Factored the quadratic

x + 7 = 0     x - 6 = 0     Applied zero product rule

     x = -7         x = 6     Solved the binomials

We reject x = -7, because x must be positive

    x = 6

x + 1 = 7

Check:

6(6+ 1) = 42

   6(7) = 42

     42 = 42

OK.

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