Question

Problem: Given that the sum of two roots of x4 - 2x3 + 4x2 +6x-21=0
is zero. Find the roots of the equation.​

Answer 1

Answer:

let α, β, γ, δ are the roots of given equation, since sum of two is zero.

α + β = 0

now α + β + γ + δ = 2 ⇒ γ + δ = 2

let αβ = p, γδ = q

the equation having the roots α, β is x2 – (α + β) x + αβ = 0

∴ x2 + p = 0

the equation having the roots γ, δ is x2 – (γ + δ)x + γδ = 0

∴ x2 – 2x + q = 0

∴ x4 – 2x3 + 4x2 + 6x – 21

= (x2 + p) (x2 – 2x + q)

= x4 – 2x3 + x2(p + q) – 2px + pq

comparing the like terms

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