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Formation of a Quadratic Equation From It's Roots

α, β are zero...

Question

α,β are zeros of polynomial 2x^2+6x-3 find the value of:-- α^3β+β^3α,[ α_β]^2,α+1/α+β1/β,α^2/β+β^2β,1/α+1/β

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α

β

x^{2} - 3 x - 2

then find quadratic polynomial whose zeros are

1) \frac{1}{2} α + β

\frac{1}{2} β + α

2) α - \frac{1}{α} + 1

β - \frac{1}{β} + 1

α

β

are the zero of the quadratic polynomial

p (x) = 4 x^{2} - 5 x - 1

α^{2} β^{2} + α β^{2} .

α

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - 2 x + 3

, find a polynomial whose roots are
(i)

α + 2, β + 2

\frac{α - 1}{α + 1}, \frac{β - 1}{β + 1} .

α, β, γ

are the zeroes of polynomial

P (x) = x^{3} + 4 x + 2

, then find the value of

\frac{1}{α + β} + \frac{1}{β + γ} + \frac{1}{γ + α}

α, β, γ

are the zeroes of the cubic polynomial

x^{3} + 4 x + 2

, then find the value of:

\frac{1}{α + β} + \frac{1}{β + γ} + \frac{1}{γ + α}

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Formation of a Quadratic Equation From It's Roots

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