If α and β are the roots of the equation 3x2 + bx − 2 = 0. Find the value of 1α 1 α + 1β

Question 1 Report

If α and β are the roots of the equation 3x2 + bx − 2 = 0. Find the value of $\frac{1}{α}$ + $\frac{1}{β}$

\frac{- 5}{3}

\frac{- 2}{3}

\frac{1}{2}

\frac{5}{2}

Answer Details

\frac{1}{α}

+

\frac{1}{β}

=

\frac{β - α}{α β}

3x2 + 5x + 5x − 2 = 0.
Sum of root = α + β
Product of root = αβ
x2 +

\frac{5 x}{3}

−

\frac{2}{3}

= 0
αβ = −

\frac{- 2}{3}

α + β =

\frac{5}{3}

∴

\frac{α + β}{α β}

= −

\frac{\frac{5}{3}}{\frac{2}{3}}

= −

\frac{2}{3}

×

\frac{3}{3}

=

\frac{5}{2}

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