Question

The roots of the quadratic equation px² – qx + r = 0 are real and equal if ______.

Options

• p² = 4qr

• q² = 4pr

• –q² = 4pr

• p² > 4pr

Answer 1

The roots of the quadratic equation px² – qx + r = 0 are real and equal if q² = 4pr.

Explanation:

Given, equation is px² – qx + r = 0

On comparing it with ax² + bx + c = 0, we get

a = p, b = –q, c = r

For roots to be equal, D = 0

i.e., b² – 4ac = 0

`\implies` (–q)² – 4 × p × r = 0

`\implies` q² – 4pr = 0

`\implies` q² = 4pr