1.

If α and β are the roots of 4x2 + 3x + 7 = 0, then the value of  \(\frac{1}{α} + \frac{1}{β}\)  isA. \(\frac{4}{7}\) B. \(-\frac{3}{7}\) C.  \(\frac{3}{7}\)  D. \(-\frac{3}{4}\) 

Answer»

Given 4x2+ 3x + 7 = 0 

We know sum of the roots = \(\frac{-3}{4}\)

Product of the roots =  \(\frac{7}{4}\)

As given that α and β are roots then,

α + β  =  \(\frac{-3}{4}\) 

α β =  \(\frac{7}{4} \)  

Given \(\frac{1}{α} + \frac{1}{β}\) 

\(\frac{α+β}{αβ}\) 

= \(-\frac{3}{\frac{4}{\frac{7}{4}}}\) 

\(\frac{-3}{7}\)



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