Find the polynomial equation of the lowest degree in terms of a whose roots are -3 and 8.

Question: Find the polynomial equation of the lowest degree in terms of a whose roots are -3 and 8.

Solution:
Let,
The roots are α = - 3 and β = 8 .
Thus, the corresponding polynomial equation is,
⇒ a² - (α + β)a + αβ = 0
⇒ a² - (- 3 + 8)a + (- 3)8 = 0
⇒ a² - 5a - 24 = 0