If $α, β$ are the zeroes of the polynomials $2 y^{2} + 7 y + 5$ , then find the value of $α + β + α β .$

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Solution

Given polynomial $2 y^{2} + 7 y + 5$

Here $a = 2, b = 7, c = 5$

$α, β$ are two zeroes

So, sum of the zeroes $= α + β = - \frac{b}{a}$
$= \frac{- 7}{2}$

Product of the zeroes $= α β = \frac{c}{a}$

$= \frac{5}{2}$

Now just put the values

$α + β + α β = (α + β) + α β$

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

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

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

$= - 1$

$∴$ So, the required answer is $- 1$ .

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