Answer:
k = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Using the determinant Δ = b² - 4ac to determine the value of k
The condition for the equation to have 2 equal real roots is
b² - 4ac = 0
Given
(k + 1)x² - 6x + 5 = 0 ← in standard form
with a = k + 1, b = - 6 and c = 5, then
(- 6)² - 4(k + 1) × 5 = 0, that is
36 - 20(k + 1) = 0 ← distribute and simplify left side
36 - 20k - 20 = 0
16 - 20k = 0 ( subtract 16 from both sides )
- 20k = - 16 ( divide both sides by - 20 )
k = [tex]\frac{-16}{-20}[/tex] = [tex]\frac{4}{5}[/tex]
