Answer:
b = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Using the discriminant for nature of roots ( x- intercepts )
If b² - 4ac = 0 then roots are real and equal ( that is only 1 x- intercept )
Given
f(x) = x² - 2bx + b² + 2b - 1
with a = 1, b = - 2b and c = b² + 2b - 1, then
(- 2b)² - 4(b² + 2b - 1) = 0 ← distribute and simplify left side
4b² - 4b² - 8b + 4 = 0
- 8b + 4 = 0 ( subtract 4 from both sides )
- 8b = - 4 ( divide both sides by - 8 )
b = [tex]\frac{1}{2}[/tex]
