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Formation of a Quadratic Equation From It's Roots

If α and β ar...

Question

If α and β are the zeros of the polynomial f(x) = x² + px + q, from a polynomial whose zeros are (α + β)² and (α − β)².

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Solution

If and are the zeros of the quadratic polynomial

Let S and P denote respectively the sums and product of the zeros of the polynomial whose zeros are and. Then,

The required polynomial of is given by

, where k is any non-zero real number.

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Formation of a Quadratic Equation From It's Roots

Standard X Mathematics

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