SAT Math Practice Question #1306 (Hard (720)) | Test Citadel
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SAT Math Difficulty: Hard (720)

Digital SAT Math Practice Question #1306

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

In the $xy$-plane, the line $y = 3x - 5$ intersects the parabola $y = x^2 - 2x + 1$ at points $(x_1, y_1)$ and $(x_2, y_2)$. What is the value of $x_1 + x_2$?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Vieta's shortcut: Set $x^2 - 2x + 1 = 3x - 5 \implies x^2 - 5x + 6 = 0$. Sum of roots is $-b/a = -(-5)/1 = 5$ without factoring!

Masterclass Solution & Distractor Trap Analysis

Set the equations equal: $x^2 - 2x + 1 = 3x - 5 \implies x^2 - 5x + 6 = 0$. By Vieta's formulas, for a quadratic equation $ax^2 + bx + c = 0$, the sum of the roots is $-b/a = -(-5)/1 = 5$....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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