JAMB 2000 · UME · Q22

If $\alpha$ and $\beta$ are the roots of the equation $3x^2 + 5x - 2 = 0$ , find the value of $\frac1\alpha + \frac1\beta$ .

Worked solution (try it first)

For $ax^2 + bx + c = 0$ , the sum of the roots is $-\frac ba$ and the product is $\frac ca$ .
So $\alpha + \beta = -\frac53$ and $\alpha\beta = -\frac23$ .
Add the fractions: $\dfrac1\alpha + \dfrac1\beta = \dfrac{\alpha + \beta}{\alpha\beta}$ .
So the value is $-\frac53 \div \left(-\frac23\right) = \frac52$ , option D.