Theory of Equations 1 Question 39
40. If the products of the roots of the equation $x^{2}-3 k x+2 e^{2 \log k}-1=0$ is 7 , then the roots are real for $k=\ldots$.
(1984, 2M)
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Solution:
- Since, $x^{2}-3 k x+2 e^{2 \log k}-1=0$ has product of roots 7 .
$$ \begin{array}{rlrl} \Rightarrow & 2 e^{2 \log k}-1 & =7 \\ \Rightarrow & e^{2 \log _e k} & =4 \\ \Rightarrow & & k^{2} & =4 \end{array} $$
$$ \Rightarrow \quad k=2 \quad \text { [neglecting }-2] $$
