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
