Determine whether and are the solutions of the equation 6x² — x — 12 = 0 or not.

Represent the following situations in the form of the quadratic equation.

The hypotenuse of a right-angled triangle is 6 metres more than twice of the shortest side. The third side is two metres less than the hypotenuse.

Represent the following situations in the form of the quadratic equation.

A piece of cloth costs Rs. 200. If the piece was 5 metre longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged.

Determine whether (i) x = 1, (ii) x = 3 are the solutions of the equation x² — 5x + 4 = 0 or not.

Determine whether x = √3 and x = —2√3 are solutions of the equation x² – 3√3x + 6 = 0