if alpha and beta are the zeros of the polynomial x square minus a X + a then find the value of (1)alpha^4-beta^4 (2)-1/alpha^3+1/beta^3 (3)alpha/beta^2 + beta/ alpha^2 (4)1/alpha+1/beta-2

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(1) If alpha and beta are the zeroes of the polynomaial 2X(square)-5X+7 , Find a polynomial whose zeroes are 2 alpha + 3 beta and 3 alpha + 2 beta.

(2) If alpha and beta are the zeroes of the polynimial 3X(square)-4X+1 , Find a polynomial whose zeroes are alpha(square) by (divided by ) beta and beta (square) by alpha.

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Q. If

α, β

are the zeros of the polynomial

f (x) = x^{2} - 3 x + 6,

then find the value of

\frac{1}{α} + \frac{1}{β} + α^{2} + β^{2} - 2 α β

Q. If α and β are the zeros of the quadratic polynomial f(x) = x² − x − 4, find the value of

\frac{1}{α} + \frac{1}{β} - αβ

Q. If α and β are the zeros of the quadratic polynomial f(x) = x² − 2x + 3, find a polynomial whose roots are (i) α + 2, β + 2 (ii)

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

Q. If

α

and

β

are zeros of

x^{2} - 3 x - 2

then find quadratic polynomial whose zeros are

1) \frac{1}{2} α + β

and

\frac{1}{2} β + α

2) α - \frac{1}{α} + 1

and

β - \frac{1}{β} + 1

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