# Wilma is thinking of 2 numbers. The sum is 2 and the product is -24. Use a quadratic equation to find the two numbers. This is an Algebra II word problem. 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` .

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