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Definition of Functions

If α and ...

Question

If $α$ and $β$ are zeroes of the polynomial $2 x^{2} + 7 x + 3$ , then find the value of $α^{2} + β^{2} - 2 α β$ .

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Solution

$2 x^{2} + 7 x + 3$
$α, β$ are roots
$α + β = - \frac{7}{2}, α β = \frac{3}{2}$
$α^{2} + β^{2} - 2 α β = (α + β)^{2} - 2 α β - 2 α β = (α + β)^{2} - 4 α β = (\frac{- 7}{2})^{2} - 4 (\frac{3}{2})$
$α^{2} + β^{2} - 2 α β = \frac{25}{4}$

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