If $α$ and $β$ are the zeros of the polynomial $2 x^{2} + 3 x^{2} + 5$ , then find value of $\frac{α + β}{α β}$ .

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Solution

Given quadratic polynomial is $2 x^{2} + 3 x + 5.$
$p (x) = 2 x^{2} + 3 x + 5.$

sum of roots $= α + β = \frac{- b}{a}$
$= \frac{- 3}{2}$

product of roots = $α β = \frac{c}{a}$
$= \frac{5}{2} .$

Therefore substituting these values

$\frac{α + β}{α β} = \frac{\frac{- 3}{2}}{\frac{5}{2}}$

$= \frac{- 3}{2} \times \frac{2}{5}$

$= \frac{- 3}{5}$

$∴ \frac{α + β}{α β} = \frac{- 3}{5} .$

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