Question

What two numbers have a product of -32 and a sum of 14?

Answer 1

16 and - 2

Explanation:

let the 2 numbers be x and y, then

xy = - 32 → (1)

x + y = 14 → (2)

Subtract y from both sides of (2)

x = 14 - y → (3)

Substitute x = 14 - y into (1)

(14 - y)y = - 32 ← distribute left side

14y - y² = - 32 ( add 32 to both sides )

14y - y² + 32 = 0 ( multiply through by - 1 )

y² - 14y - 32 = 0 ← in standard form

(y - 16)(y + 2) = 0 ← in factored form

Equate each factor to zero and solve for y

y - 16 = 0 ⇒ y = 16

y + 2 = 0 ⇒ y = - 2

Substitute these values into (3) for corresponding value of x

y = 16 → x = 14 - 16 = - 2

y = - 2 → x = 14 - (- 2) = 14 + 2 = 16

Thus the2 numbers are 16 and - 2