Mathematics

Problem

For the quadratic equation

(k^{2} - 9)x^{2} + 6x + 1 = 0

, the coefficient of

x^{2}

is required to be positive and the equation must have two distinct real roots. Which of the following ranges of

k

satisfies both conditions? a)

|k|<3

3<k<3\sqrt{2}

-3\sqrt{2}<k<-3\; \text{or}\; 3<k<3\sqrt{2}

|k|>3\sqrt{2}