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Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

If α and ...

Question

If $α$ and $β$ are the zeroes of the polynomial $6 y^{2} - 7 y + 2$ ; find a quadratic polynomial whose zeroes are $\frac{1}{α} + \frac{1}{β}$ .

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Solution

Let p(y) = 6 y²- 7y + 2

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Q. Find a quadratic polynomial whose zeroes are

\frac{1}{α}

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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}

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find the polynomial whose zeroes are

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