Question

The product of 2 numbers is -24 and their sum is -5. What are the two numbers and why are they the two numbers?

Answer 1

The numbers are (-8, 3) or (3, -8).

Step-by-step explanation:

• Step 1: Given the product of the numbers are -24 and their sum are -5. Let the numbers be a and b. Form equations out of these details.

⇒ a + b = -5 ⇒ b = -5 - a

⇒ a × b = -24 -------- (1)

• Step 2: Substitute the value of b in eq(1)

⇒ a × (-5 - a) = - 24

⇒ -5a - a² = -24

⇒ a² + 5a - 24 = 0

• Step 3: Solve the quadratic equation for a.

a = (-5 ± √25 - 4 × 1 × -24)/2

  = (-5 ± √121)/2

  = - 16/2, 6/2 = -8 or 3

• Step 4: For each value of a, find b.

When a = -8, b = -5 +8 = 3

When a = 3, b = -5 - 3 = -8.