Answer:
p = - [tex]\frac{2}{3}[/tex] , p = 2
Step-by-step explanation:
Using the discriminant to solve for p
Δ = b² - 4ac
The condition on the discriminant for 2 eeal and equal roots is
b² - 4ac = 0
Given
p²x² - (p + 2)x + 1 = 0
with a = p² , b = - (p + 2) , c = 1 , then
(- (p + 2) )² - 4p² = 0
(p + 2)² - 4p² = 0
p² + 4p + 4 - 4p² = 0
- 3p² + 4p + 4 = 0 ( multiply through by - 1 )
3p² - 4p - 4 = 0 ← in standard form
(3p + 2)(p - 2) = 0 ← in factored form
Equate each factor to zero and solve for p
3p + 2 = 0 ⇒ 3p = - 2 ⇒ p = - [tex]\frac{2}{3}[/tex]
p - 2 = 0 ⇒ p = 2
