If and are the roots of the equation 3x
2 + bx 2 = 0. Find the value of \(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\)
A. \(\frac{-5}{3}\)
B. \(\frac{-2}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{5}{2}\)
Correct Answer: D
Explanation
\(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\) = \(\frac{\beta -\alpha}{\alpha \beta}\)
3x2 + 5x + 5x − 2 = 0.
Sum of root = α + β
Product of root = αβ
x2 + \(\frac{5x}{3}\) − \(\frac{2}{3}\) = 0
αβ = − \(\frac{-2}{3}\)
α + β = \(\frac{5}{3}\)
∴ \(\frac{\alpha + \beta}{\alpha \beta}\) = − \(\frac{\frac{5}{3}}{\frac{2}{3}}}\)
= − \(\frac{2}{3}\) × \(\frac{3}{3}\)
= \(\frac{5}{2}\)
