Jambmaths question:
If $\alpha \text{ and }\beta $are roots of the equation $3{{x}^{2}}+5x-2=0$. Find the value of $\tfrac{1}{\alpha }+\tfrac{1}{\beta }$.(A) $-\tfrac{5}{2}$ (B) $-\tfrac{3}{2}$ (C) $\tfrac{1}{2}$ (D)$\tfrac{5}{2}$
Option A:
$-\tfrac{5}{2}$
Option B:
$-\tfrac{3}{2}$
Option C:
$\tfrac{1}{2}$
Option D:
$\tfrac{5}{2}$
Jamb Maths Solution:
$\begin{align} & 3{{x}^{2}}+5x-2=0 \\ & a=3,\text{ }b=5,\text{ }c=-2 \\ & \text{Sum of roots}=\alpha +\beta =-\tfrac{b}{a}=-\tfrac{5}{3} \\ & \text{Product of roots}=\alpha \beta =\tfrac{c}{a}=-\tfrac{2}{3} \\ & \frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{-\tfrac{5}{3}}{-\tfrac{2}{3}}=\frac{5}{3}\times \frac{3}{2}=\frac{5}{2} \\\end{align}$
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