Question

Q: alpha and beta are the zeroes of the quadratic polynomial f(x)= ax²+bx+c , then evaluate
polynomial
I) alpha2 +beta2
ii) alpha3 +beta3​

Answer 1

Step-by-step explanation:

alpha + beta = -b/a

alpha*beta = c/a

(1) alpha² + beta² = (alpha+beta)² - 2alpha*beta

= b²/a² - 2c/a = (b²-2ac)/a²

(2) alpha³ + beta³ = (alpha+beta)³ - 3alpha*beta (alpha+beta)

= b³/a³ - 3c/a ( -b/a)

= b³/a³ + 3bc/a² = (b³+3abc)/a³