Question

If alpha beta and gamma are the roots of equation x³-3x²+x+5=0 then ​

Answer 1

Answer:

If α, β and γ are the roots of the equation x3 - 3x2 + x + 5 = 0, then y = ∑α2 + αβγ satisfies the equation. Hence y = 2 satisfies the equation y3 – y2 – y – 2 = 0.∑α = 3

∑α = 3∑αβ = 1

∑α = 3∑αβ = 1αβγ = – 5

∑α = 3∑αβ = 1αβγ = – 5y = ∑α2 + αβγ = (∑α)2 – 2 ∑αβ + αβγ

∑α = 3∑αβ = 1αβγ = – 5y = ∑α2 + αβγ = (∑α)2 – 2 ∑αβ + αβγ= 9 – 2 (1) + (- 5)

∑α = 3∑αβ = 1αβγ = – 5y = ∑α2 + αβγ = (∑α)2 – 2 ∑αβ + αβγ= 9 – 2 (1) + (- 5)y = 2

∑α = 3∑αβ = 1αβγ = – 5y = ∑α2 + αβγ = (∑α)2 – 2 ∑αβ + αβγ= 9 – 2 (1) + (- 5)y = 2Hence y = 2 satisfies the equation y3 – y2 – y – 2 = 0.