SAT Math Practice Question #528 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #528

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

The equation \( \frac{x^2 - cx + 12}{x - 4} = 2 \) has exactly one real solution for \( x \). If \( c \) is an integer, what is the value of \( c \)?
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Socratic AI Engine Step-by-Step Derivation
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Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

To solve this problem, we need to understand the conditions under which a rational equation simplifies to have exactly one real solution. Let's start by clearing the denominator. Assume \( x eq 4 \) (since that would make the denominator ze...

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

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