Question

If alpha, beta , y are the zeroes of cubic polynomial x3+5x^ 2 +4 then alpha+beta+y=​

Answer 1

Step-by-step explanation:

If alpha, beta, gamma are zeros of cubic polynomial x^3 + 5x - 2, what is the value of alpha^3 + beta^3 + gamma^3?

x³ + 5x – 2

a=1, b=0, c=5, d= - 2

Comparing we get

α+ β+γ = -b/a=0

αβ + αγ+β γ=c/a=5

αβγ=-d/a = 2

Since α,β,γ are zeroes of given equation

So α ³ + 5 α – 2 =0 ⇒ α ³ = 2-5 α…….(1)

β³ + 5β – 2=0 ⇒ β ³ = 2-5 β………(2)

γ ³ + 5 γ – 2 =0⇒ γ ³ = 2-5 γ…….(3)

Adding (1) (2) & (3)

α ³ + β ³ + γ ³ = 6-5(α+ β+γ)

α ³ + β ³ + γ ³ = 6-5(0)=6

α ³ + β ³ + γ ³ = 6

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Answer 2

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