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Properties of Determinants

The equation ...

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The equation 3^2x+1 - 14 - 3^x+1 = √(1 + 9^x + 6 × 3^x-1) (a)2 real roots (b)1 real and 1 extraneous root (c)Only 1 real root (d)No real root

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Q. The equation

3^{2 x + 1} - 14 - 3^{x + 1} = \sqrt{1 + 9^{x} + 6 \times 3^{x - 1}}

Q. The sum of real roots of the equation

(x - 1) (x - 2) (3 x - 1) (3 x - 2) = 8 x^{2}

Q. The real number k for which the equation,

2 x^{3} + 3 x + k = 0

has two distinct real roots in [0, 1]

Q. The number of real roots of the equation

\frac{x^{2} - 3 x}{x^{2} - 1} + 2 + \frac{1}{x - 1} = 0

(2 x^{2} - 3 x + 1) (2 x^{2} + 5 x + 1) = 9 x^{2}

, then the absolute value of the sum of all real roots of the equation is:

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Properties of Determinants

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