Question

x²+px+q=0 , find alpha³+ beta
URGENT!
Don't post irrelevant answers...​

Answer 1

Answer:

a³ + b³ = (-p³ + 3pq)

Step-by-step explanation:

x² + px + q = 0

ax² + bx + c = 0

a = 1, b = p, c = q

Let the zeros be a and b

Sum of zeros = -b/a = -p/1 = -p (a + b)

Product of zeros = c/a = q/1 = q (ab)

a³ + b³ = (a + b)(a² - ab + b²)

= (a + b)((a + b)² - 2ab - ab) (Think about it.......)

= (-p)((-p)² - 2(q) - q)

= (-p)(p² - 3q)

= -p³ + 3pq

Thus, a³ + b³ = (-p³ + 3pq)

Hope you understood it........All the best