Find the values of k for which the quadratic equation 2x^2 − (k + 2)x + k = 0 has real and equal roots.

k = 2

Step-by-step explanation:

If the roots are real and equal then the condition for the discriminant is

b² - 4ac = 0

For 2x² - (k + 2)x + k = 0 ← in standard form

with a = 2, b = - (k + 2) and c = k, then

(- (k + 2))² - (4 × 2 × k ) = 0

k² + 4k + 4 - 8k = 0

k² - 4k + 4 = 0

(k - 2)² = 0

Equate factor to zero and solve for k

(k - 2)² = 0 ⇒ k - 2 = 0 ⇒ k = 2

Step-by-step explanation:

A quadratic equation has two equal real roots if a discriminant is equal 0.

Discriminant

We have the equation

Substitute:

1     sepan

2     encuentren

3     tenga

4     hable

5   parezca

6   llegue