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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Answer:
Correct Answer: 40. (k=2)
Solution:
- Since, $x^{2}-3 k x+2 e^{2 \log k}-1=0$ has product of roots 7 .
$\Rightarrow 2 e^{2 \log k}-1 =7 $
$\Rightarrow e^{2 \log _e k} =4 $
$\Rightarrow k^{2} =4$
$ \Rightarrow k=2 \quad \text { [neglecting }-2] $
