Question

Show that the following equation has repeated roots:

9x² − 6x + 1 = 0

Answer 1

Given:

9x² − 6x + 1 = 0

Identify coefficients

From the standard quadratic form ax² + bx + c = 0:

a = 9

b = −6

c = 1

Use the discriminant formula

D = b² − 4ac

D = (−6)² − 4(9) (1)

= 36 − 36

= 0

Since D = 0, the quadratic equation has real and equal roots, also called repeated roots.

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

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

`= (-(-6))/2.9`

`= 6/18`

`=1/3`