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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 $2 y^{2} + 7 y + 5$ , write the values of $α + β + α β$ .

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Solution

$α & β$ ax zeros of $2 y^{2} + 2 y + 5$

Now sum of roots $= α + β = - \frac{7}{2}$

Product $= α β = \frac{5}{2}$

$α + β + α β$

$= - \frac{7}{2} + \frac{5}{2}$

$= - \frac{2}{2} = - 1$

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