Question

If alpha beta and gamma are the zeros of p(x)=x³p(x)=x³-5x²+11x-5. Find the value of alpha²+ beta ²+ gamma².​

Answer 1

α, β and γ are zeroes of the Polynomial x³–5x²+11x-5.

Now, We've to find the different relations b/w the zeroes of the Polynomial.

→ α+β+γ = –b/a

→ α+β+γ = –(-5)/1

→ α+β+γ = 5/1

→ α+β+γ = 5

→ αβ+βγ+γα = c/a

→ αβ+βγ+γα = 11/1

→ αβ+βγ+γα = 11

Now, we're going to find that what is the value of alpha²+ beta ²+ gamma².

→ (α+β+γ)² = α²+β²+γ²+2(αβ+βγ+γα)

→ (5)² = α²+β²+γ²+2(11)

→ 25 = α²+β²+γ²+22

→ 25 – 22 = α²+β²+γ²

→ α²+β²+γ² = 3

Hence,

The value of alpha²+ beta ²+ gamma² is 3.

Answer 2

see the above attachment