Çözüldü Function Tangent to x-Axis - Undetermined Coefficients Rule - Derivative

https://i.servimg.com/u/f72/19/97/10/39/sat46.png
SAT Math Level II
https://z-library.sk/book/ZjKrYz4NR0/sat-math-level-ii.html
[Page 14 (22 in the pdf file), Example Question]
---
Using Undetermined Coefficients:
a, b ∈ R
2x^2 + p·x + 1 ≡ (a·x + b)^2 = a^2·x^2 + 2·a·b·x + b^2
2 = a^2 ⇒ a = ∓√2
1 = b^2 ⇒ b = ∓1
p = 2·a·b = ∓2·√2
---
Using Derivative:
f '(x) = 4x + p = 0 ⇒ x = -p / 4
f(-p / 4) = 2(p^2 / 16) - p^2 / 4 + 1 = 0 ⇒ p^2 = 8 ⇒ p = ∓2·√2.