Method of Solving a Quadratic Equation

Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.

Solve the following quadratic equations by factorization:

a²b²x² + b²x - a²x - 1 = 0

Solve : x² – 11x – 12 =0; when x ∈ N

If `sqrt (2/3)` is a solution of equation 3x² + mx + 2 = 0, find the value of m.

If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?

One of the roots of equation 5m² + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.

The area of right-angled triangle is 600cm². If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.

Solve the following quadratic equation by factorisation.

\[6x - \frac{2}{x} = 1\]