First slide

Theory of equations

Question

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

Moderate

A

7
B

8
C

9
D

10

Solution

$\begin{array}{l} p = 2 e^{4 \ln k} - 1 = 31 \\ e^{\ln (k)^{4}} = 16 \\ k = \pm 2 \\ As k = \pm 2, so k = + 2 \\ Now, sum = 5 k = 5 \times 2 = 10 \end{array}$

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