How do you describe the nature of the roots of the equation #x^2-4x+4=0#?

1 Answer
Oct 17, 2017

Answer:

We can factor the expression on the right as:

#(x - 2)(x - 2) = 0# or #(x - 2)^2 = 0#

Therefore the two roots for this quadratic are the same: #x = 2#

Explanation:

We can also use the discriminate to show this same result:

The quadratic formula states:

For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#

The discriminate is the portion of the quadratic equation within the radical: #color(blue)(b)^2 - 4color(red)(a)color(green)(c)#

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

#color(red)(1)# for #color(red)(a)#

#color(blue)(-4)# for #color(blue)(b)#

#color(green)(4)# for #color(green)(c)#

#color(blue)((-4))^2 - (4 * color(red)(1) * color(green)(4)) =>#

#16 - 16 =>#

#0#

Because the discriminate is #0# you get just ONE solution.