Find two integers whose and whose PRODUCT IS SUM IS ANSWER a)

step 1 In this problem, we're being asked to find two integers whose product is given in the first colu

Find two integers whose and whose PRODUCT...

Find two integers whose
$\begin{array}{cccc} & & \text { and whose } & \\ & \text { PRODUCT IS } & \text { SUM IS } & \text { ANSWER } \\ \text { a) } & -50 & 5 & \\ \text { b) } & 27 & -28 & \\ \text { c) } & 12 & 8 & \\ \text { d) } & -72 & -6 & \end{array}$

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Key Concepts

Vieta's Formulas

Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. For a quadratic equation of the form x² - (sum)x + (product) = 0, the sum of the roots is equal to the coefficient of x (with the opposite sign) and the product of the roots is equal to the constant term. This concept is essential when finding two integers that satisfy a given sum and product.

Quadratic Equations

Constructing and solving a quadratic equation is a systematic method to find two unknown integers given their sum and product. By using the relationship x² - (sum)x + (product) = 0, you can solve for x using factorization or the quadratic formula, which yields the two integers as its roots.

Integer Factorization

Integer factorization involves identifying pairs of factors of a given product and checking if these pairs add up to the specified sum. This method is particularly useful when dealing with problems that require finding integer solutions, as it often leads to a quicker, more straightforward answer than solving a quadratic equation.

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