If and are the roots of the equation 3x2 bx 2 0... - JAMB Mathematics 2017 Question
If α and β are the roots of the equation 3x2 + 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
\(\frac{5}{2}\)
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Correct Option: D
(\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})
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