Question

Find the value(s) of p for which the quadratic equation given as (p + 4) x² − (p + 1) x + 1 = 0 has real and equal roots. Also, find the roots of the equation(s) so obtained.

The value of 'a' for which ax² + x + a = 0 has equal and positive roots is :

Find the value(s) of 'k' so that the quadratic equation 4x² + kx + 1 = 0 has real and equal roots.

A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and the walkway is 360 square metres. The width of the walkway is same on all sides. The dimensions of the lawn itself are 12 metres by 10 metres.