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Question

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) α-1α+1, β-1β+1.

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Solution

(i) Since and are the zeros of the quadratic polynomial

Product of the zeros =

Let S and P denote respectively the sums and product of the polynomial whose zeros

Therefore the required polynomial f (x) is given by

Hence, the required equation is.

(ii) Since and are the zeros of the quadratic polynomial

Product of the zeros =

Let S and P denote respectively the sums and product of the polynomial whose zeros

By substituting and we get ,

The required polynomial f (x) is given by,

Hence, the required equation is , where k is any non zero real number .


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