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Test Citadel features an authentic Bluebook-calibrated countdown timer with visibility toggle, question navigation grid, choice eliminator cross-out tool, embedded Desmos graphing calculator, and official College Board formula sheets.

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Yes. Every visitor can complete 4 free diagnostic problems (2 Math with Desmos and 2 Reading & Writing) with full Socratic explanations before upgrading to Citadel Pro.

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Citadel Pro grants unlimited access to 2,600+ adaptive questions, multi-tier Socratic hint trees, Desmos graphing shortcuts, distractor trap breakdowns, and simulated full-length SAT and ACT exams.

SAT Math Difficulty: Hard (800) • Calibrated to 2026 Testing Standard

Digital SAT Math Practice Question #339

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

Let $ P(x) = x^4 + ax^3 + bx^2 + cx + d $, where $ a, b, c, $ and $ d $ are real constants. If two of the roots of the equation $ P(x) = 0 $ are $ 3 - 2i $ and $ -1 + i $, what is the value of $ b $?

Select Your Answer:

Socratic AI Engine Step-by-Step Derivation

0ms Precomputed

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

This polynomial question takes no prisoners! It tests the Complex Conjugate Root Theorem and advanced algebraic expansion. Here is the step-by-step masterclass on how to solve it. Step 1: Identify all four roots. The problem states that the...

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

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