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in Polynomials by (38.0k points)
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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) \(\frac{\alpha-1}{\alpha+1}\)\(\frac{\beta-1}{\beta+1}\)

1 Answer

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Best answer

(i) f(x) = k(x2 - 6x + 11)

A quadratic equation when sum and product of its zeros is given by:

, where k is a constant 

Sum of the roots

Product of the roots 

Sum of the zeros of new equation

α + β + 4 = 2 + 4 = 6

Product of the zeros of new equation

(ii) A quadratic equation when sum and product of its zeros is given by:

, where k is a constant

Sum of the roots

Product of the roots

Sum of the zeros of new equation

Product of the zeros of new equation

Therefore equation is:

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