Mathematicsα and β are the roots of an equation x2−ax+b=0, then α2+αβ+β2 is

$α$ and $β$ are the roots of an equation $x^{2} - a x + b = 0$ , then $α^{2} + α β + β^{2}$ is

$α, β$ are the roots of an equation $x^{2} - a x + b = 0$

$α + β = a$ and $α β = b$

$α^{2} + β^{2} + α β = {(α + β)}^{2} - 2 α β + α β$

$= {(α + β)}^{2} - α β$

$= a^{2} - b$

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