Use the discriminant to describe the roots of each equation. Then select the best description. x2 - 4x + 4 = 0

Question

Use the discriminant to describe the roots of each equation. Then select the best description.

x2 - 4x + 4 = 0

Answer 1

x²-4x + 4 = 0

 

The discriminant is the part under the square root in the quadratic formula

x = (-b ±√(b²-4ac))/2a

The discriminant is b²-4ac

 

If b²-4ac > 0  then there are two real roots

If b²-4ac = 0  there is 1 real root = -b/2a

If b²-4ac < 0 there are two roots which are complex conjugates

                    of the format  a ± bi

 

In this case b²-4ac = (-4)²-4(1)(4) = 16 - 16 = 0

 

Since the discriminant = 0 there is one real root

 

That root is  -b/2a = -(-4)/2 = 4/2 = 2

 

There is only one real root so the graph only touches the x axis

at one point... (2,0).  Since the coefficient of the square term is

positive this graphs as a parabola with vertex at (2,0) opening

upwards.

 

 

Answer 2

The discriminant is the square-root part in the quadratic formula.

 

√(b² - 4ac)

 

 

where:

a = 1

b = -4

c = 4

 

 

b² < 4ac    indicates that the roots are complex.

b² > 4ac    indicates that the roots are real.

b² = 4ac    indicates that the roots repeat.