First slide

Theory of equations

Question

If the product of the roots of the equation
$x^{2} - 5 k x + 2 e^{4 \ln k} - 1 = 0 is 31$ then sum of the root is

Moderate

A

-10
B

5
C

-8
D

10

Solution

We have product of the roots
$= 2 e^{4 \ln k} - 1 = 31$ (given)
$\begin{array}{l} \Rightarrow e^{4 \ln k} = 16 \\ \Rightarrow k^{4} = 16 \Rightarrow k^{4} - 16 = 0 \\ \Rightarrow (k - 2) (k + 2) (k^{2} + 4) = 0 \\ \Rightarrow k = 2, - 2 \end{array}$
As k > 0, we get k = 2.
Sum of the roots = 5k = 10

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