### Instruction: Let the reciprocals of the roots of $5x^2 + 3x + 4$ be $\alpha$ and $\beta$. Evaluate $\alpha + \beta$.### Response: So we want to find the sum of the reciprocals of the roots of $5x^2 + 3x + 4$.
Let's call the roots $r$ and $s$.
So the reciprocals of the roots are $1/r$ and $1/s$.
And we want to find $(1/r) + (1/s)$.
That's equal to $(r + s)/rs$.
We know that $r + s = -3/5$.
And we know that $rs = 4/5$.
So the sum of the reciprocals of the roots is $(-3/5)/(4/5)$.