Mathematicsif α,β are the roots of the equation x2+3x+1=0, then the value of αβ+βα=

if $α, β$ are the roots of the equation $x^{2} + 3 x + 1 = 0$ , then the value of $\frac{α}{β} + \frac{β}{α} =$

$α + β = - 3, α β = 1$

$\frac{α}{β} + \frac{β}{α} = \frac{α^{2} + β^{2}}{α β}$

$= \frac{{(α + β)}^{2} - 2 α β}{α β} = \frac{{(- 3)}^{2} - 2.1}{1}$

$= 9 - 2 = 7$

Related content