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  4. If α and β are the roots of the equation x 2+3x-4 =0, then (1/α)+(1/β) is equal to

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Q. If $\alpha$ and $\beta$ are the roots of the equation $x ^{2}+3x-4 =0,$ then $\frac{1}{\alpha}+\frac{1}{\beta}$ is equal to

KEAMKEAM 2014

Solution:

Since, $\alpha$ and $\beta$ are the roots of the equation
$x^{2}+3 x-4=0$
Then,$\alpha+\beta=-3$ and $\alpha \beta=-4$
Now, $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}=\frac{-3}{-4}=\frac{3}{4}$