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

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

Solution:
Let,
The roots are α = - 3 and β = 8.

Thus, the corresponding polynomial equation is,
x² - (α + β)x + αβ = 0
⇒ x² - ( - 3 + 8)x + (- 3) . 8 = 0
∴ x² - 5x - 24 = 0