If $$x = \left(2 - \sqrt{3}\right)^{-1},$$​ then the value of $$x^3 - 2x^2 - 7x + 5$$​ is-

The sum of squares of all the roots of the equation:
​$$\left(x + \frac{1}{x}\right)^2 - 4 = \frac{3}{2} \left(x - \frac{1}{x}\right), x \neq 0$$ is:

What is the remainder when the polynomial x¹⁰⁰ – 2x⁵¹ + 1 is divided by (x² – 1) ?

The marks of 16 students in math in monthly test are 0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8, then mode will be

The equation whose roots are $$\frac{p - q}{p + q}$$​ and $$-\frac{p + q}{p - q}$$​ will be:

The factors of polynomial $$x^3 - 6x^2 + 11x - 6$$​ are-

If $$2352 = 2^x \times 3^y \times 7^z \\$$​, then the value of $$x + y + z$$​ is

Solution of $$\dfrac{x - 2}{x + 5} > 2$$​ is:

The sum of the reciprocals of the roots of the equation abx² = (a² + b² + 2ab)(x − 1) is - 

If $$x = \left(2 - \sqrt{3}\right)^{-1},$$​ then the value of $$x^3 - 2x^2 - 7x + 5$$​ is-

​$$\text{Sum and product of all roots of } 4x^3 - 8x^2 - 13x + 19 = 0 \text{ is:}$$​