Find two integers, r and s, such that their product is −12 and their sum is 1.

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: List all pairs of integers whose product is −12. We are looking for two integers, r and s, such that their product r × s = −12 and their sum r + s = 1 (from the previous problem x² + x − 12, where c = −12 and b = 1). Step 2: Calculate the product and sum for each pair of factors. Fill in the table with the factors of −12, their products, and their sums. Mark the pair that results in a sum of 1. Factors of −12 — Product of the two factors — Sum of the two factors — Result1, −12 — 1 × (−12) = −12 — 1 + (−12) = −11; −1, 12 — −1 × 12 = −12 — −1 + 12 = 11; 2, −6 — 2 × (−6) = −12 — 2 + (−6) = −4; −2, 6 — −2 × 6 = −12 — −2 + 6 = 4; 3, −4 — 3 × (−4) = −12 — 3 + (−4) = −1; −3, 4 — −3 × 4 = −12 — −3 + 4 = 1 — ✓ The two integers, r and s, are −3 and 4.

Factors of -12	Product of the two factors	Sum of the two factors	Result
$1, -12$	$1 \times (-12) = -12$	$1 + (-12) = -11$
$-1, 12$	$-1 \times 12 = -12$	$-1 + 12 = 11$
$2, -6$	$2 \times (-6) = -12$	$2 + (-6) = -4$
$-2, 6$	$-2 \times 6 = -12$	$-2 + 6 = 4$
$3, -4$	$3 \times (-4) = -12$	$3 + (-4) = -1$
$\mathbf{-3, 4}$	$\mathbf{-3 \times 4 = -12}$	$\mathbf{-3 + 4 = 1}$	✓

Find two integers, r and s, such that their product is -12 and their sum is 1.

Answer

Step-by-step solution

List all pairs of integers whose product is $-12$ .

Calculate the product and sum for each pair of factors.

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