Set 9: Quadratic Equations

Explanation

Answer: A

If $\alpha$ and $\beta$ are roots of $x^2 - 5x + 2 = 0$ , find $\alpha^2 + \beta^2$ .

✓ Correct

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use algebraic identities and Vieta's formulas. 1. Sum $\alpha + \beta = 5$ . 2. Product $\alpha\beta = 2$ . 3. Identity: $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$ . 4. Substitute: $5^2 - 2(2) = 25 - 4 = 21$ . Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is 21

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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