If the product of the roots of the equation \(x^2+4 k x+12 e^{3 \log k}-1=0,(k>0)\) is 323 , then the sum of…
If the product of the roots of the equation \(x^2+4 k x+12 e^{3 \log k}-1=0,(k>0)\) is 323 , then the sum of its roots is
\(9 k\)
12
-12
\(-16 k\)
Solution
Given quadratic equation is
\(x^2+4 k x+12 e^{3 \log k}-1=0\)
According to given information ,
Product of the roots \(=323\)
\(\begin{aligned}
& \Rightarrow \quad 12 e^{3 \log k}-1=323 \\
& \Rightarrow \quad 12 k^3=324 \Rightarrow k^3=27 \Rightarrow k=3
\end{aligned}\)
So, sum of roots \(=-4 k=-12\)
Hence, option (c) is correct.