You should use the Lagrange's resolvents to find the solutions to the quadrativ equation `x^2 - px + q = 0` .
You should know that p represents the sum of the numbers and p represents the product of the two numbers.
Since the problem provides the values of the sum and product, you may substitute the values for p and q such that:
`x^2 - x+ (-24) = 0`
`x^2 - 2x- 24 = 0`
Notice that the solutions to the quadratic equation above represent the two missing numbers.
You may solve the quadratic equation using the following quadratic formula such that:
`x_(1,2) = (-b+-sqrt(b^2-4ac))/(2a)`
Identifying the coefficients a,b,c yields:
`a = 1 , b = -2 , c = -24`
`x_(1,2) = (2+-sqrt(4 + 96))/2 => x_(1,2) = (2+sqrt100)/2`
`x_(1,2) = (2+-10)/2 => x_1 = (2+10)/2 = 6 ; x_2 = (2-10)/2 = -4`
Hence, evaluating the two missing numbers, under the given conditions, yields `x_1 = 6` , `x_2 = -4` .