Question

Show that the following equation has repeated roots:

4x² + 20x + 25 = 0

Answer 1

Given:

4x² + 20x + 25 = 0

Identify coefficients

From ax² + bx + c = 0:

a = 4

b = 20

c = 25

D = b² − 4ac

D = (20)² − 4(4)(25)

= 400 − 400

= 0

Since the discriminant D = 0, the quadratic equation has real and equal (repeated) roots.

`x = (-b)/(2a)`

`= (-20)/(2xx4)`

`= (-20)/8`

`= -5/2`