Solve 3x^2 − 12x + 12 ≤ 0.

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

Enhance your Algebra 2 Honors exam readiness. Engage with multiple choice questions, hints, and detailed explanations. Prepare effectively for your test!

Multiple Choice

Solve 3x^2 − 12x + 12 ≤ 0.

Explanation:
Treating the left side as a perfect square makes the idea clear: a square is always nonnegative, so to be less than or equal to zero it must be exactly zero. Factor the quadratic: 3x^2 − 12x + 12 = 3(x^2 − 4x + 4) = 3(x − 2)^2. The inequality becomes 3(x − 2)^2 ≤ 0. Since (x − 2)^2 ≥ 0 for all x, the only way this is ≤ 0 is when (x − 2)^2 = 0, which gives x = 2. So the value that works is 2.

Treating the left side as a perfect square makes the idea clear: a square is always nonnegative, so to be less than or equal to zero it must be exactly zero. Factor the quadratic: 3x^2 − 12x + 12 = 3(x^2 − 4x + 4) = 3(x − 2)^2. The inequality becomes 3(x − 2)^2 ≤ 0. Since (x − 2)^2 ≥ 0 for all x, the only way this is ≤ 0 is when (x − 2)^2 = 0, which gives x = 2. So the value that works is 2.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy