Question

Find the value of a and b when a+b = -5, ab = -24​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

a + b = - 5 → (1)

ab = - 24 → (2)

Rearranging (1) expressing a in terms of b, that is

a = - 5 - b → (3)

Substitute a = - 5 - b into (2)

b(- 5 - b) = - 24 ← distribute left side

- 5b - b² = - 24 ( subtract - 5b - b² from both sides )

0 = b² + 5b - 24 ← in standard form

0 = (b + 8)(b - 3) ← in factored form

Equate each factor to zero and solve for b

b + 8 = 0 ⇒ b = - 8

b - 3 = 0 ⇒ b = 3

Substitute these values into (3) for corresponding values of a

b = - 8 : a = - 5 - (- 8) = - 5 + 8 = 3

b = 3 : a = - 5 - 3 = - 8

Thus

a = 3, b= - 8 or a = - 8, b = 3

Answer 2

Step-by-step explanation:

a= - 5 - b

Subs. the above into...

ab = - 24

(-5-b)b = - 24

Therefore b=-24 or b=19