MATH SOLVE

7 months ago

Q:
# Use the discriminant to describe the roots of each equation. Then select the best description.x2 - 4x + 4 = 0double rootreal and rational rootsreal and irrational rootsnon-real roots

Accepted Solution

A:

The Discriminant of a quadratic is defined by ⇒ b² - 4ac

In our case:

a = 1 b = -4 and c = 4

Evaluate the Discriminant: (-4)² - 4(1)(4) = 16 -16 = 0

Summary of the what the Discriminant tells us:

If:

D = a positive value, then we would have two real roots

D = a negative value, then we would have no real roots

D = 0 we would exactly one real root..

In our case D = 0.. so that would imply exactly one real root, or in other words choosing from your list of options chose "double root"

You could also verify this by factoring the quadratic into (x - 2)(x -2) implying the double root of '2'

In our case:

a = 1 b = -4 and c = 4

Evaluate the Discriminant: (-4)² - 4(1)(4) = 16 -16 = 0

Summary of the what the Discriminant tells us:

If:

D = a positive value, then we would have two real roots

D = a negative value, then we would have no real roots

D = 0 we would exactly one real root..

In our case D = 0.. so that would imply exactly one real root, or in other words choosing from your list of options chose "double root"

You could also verify this by factoring the quadratic into (x - 2)(x -2) implying the double root of '2'