SOLUTION: find 4 rational numbers such that the product of the 1st 2nd and 4th is 54. The 2nd number is 2 less than the 1st number, the 3rd number is 5 less than the 2nd number and the 4th n

The equation is  

    x*(x-2)*(x-7)*(x-10) = 154,   

or

    x^4 - 19x^3 + 104x^2 - 140x - 154 = 0.


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       |     The  DIAGNOSIS  (obtained with special software  |
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Result:


The roots of the polynomial x 

    x^4 - 19x^3 + 104x^2 - 140x - 154

are


x1 = −0.31014

x2 = 2.63744

x3 = 6.47111

x4 = 10.20159


Explanation:

This polynomial has no rational roots that can be found using Rational Root Test.

Roots were found using quartic formulas.