If one root of 3x^2 + 2x + k = 0 is the reciprocal of the other, then the value of k is
If one root of 3x2 + 2x + k = 0 is the reciprocal of the other, then the value of k is
A) 3
B) -3
C) 2
D) 6
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Correct option is (A) 3
Let \(\alpha\;and\;\frac1\alpha\) are the roots of \(3x^2+2x+k=0.\)
\(\therefore\) Product of the roots \(=\frac ca=\frac k3\)
\(\Rightarrow\) \(\alpha\times\frac1\alpha=\frac k3\)
\(\Rightarrow\) \(\frac k3=1\)
\(\Rightarrow\) k = 3
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