Question

If alpha,beta and gamma are the zeroes of the polynomial x^3-5x^2+11x-5, find the value of alpha^2+beta^2+gamma^2

Answer 1

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Answer 2

Answer:

( alpha + beta + gamma)= -b/a= -5/1 = - 5

(alpha beta + beta gamma+ gamma alpha)= c/a=11/1 = 11

(alpha* beta* gamma)= -d/a = -5/1

(alpha + beta + gamma)² = α²+β² + У² = 2αβ+ 2βУ+ 2Уα

(α+β+У)²- 2(αβ+βУ+Уα) = α²+β² + У

(-5)²-2(11) = α²+β² + У

25-22 = α²+β² + У

3 = α²+β² + У