2
advanced-math

If α\alpha and β\beta are roots of x2−5x+2=0x^2 - 5x + 2 = 0, find α2+β2\alpha^2 + \beta^2.

A

21

B

25

C

29

D

23

Correct Answer: A

Choice A is the correct answer. Use algebraic identities and Vieta's formulas.

  1. Sum α+β=5\alpha + \beta = 5.
  2. Product αβ=2\alpha\beta = 2.
  3. Identity: α2+β2=(α+β)2−2αβ\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta.
  4. Substitute: 52−2(2)=25−4=215^2 - 2(2) = 25 - 4 = 21.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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Set 20: Quadratic Equations and Functions 20