Solve each equation in Exercises 83–108 by the method of your choice. $3 x^{2} - 12 x + 12 = 0$

검증된 단계별 안내

Identify the given quadratic equation: $3x^2 - 12x + 12 = 0$.

Divide the entire equation by 3 to simplify it: $x^2 - 4x + 4 = 0$.

Recognize that the simplified quadratic is a perfect square trinomial, which can be factored as $(x - 2)^2 = 0$.

Set the factor equal to zero: $x - 2 = 0$.

Solve for $x$ by adding 2 to both sides: $x = 2$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a ≠ 0. It represents a parabola when graphed and can have zero, one, or two real solutions depending on the coefficients.

Factoring and Simplification

Factoring involves rewriting a quadratic equation as a product of simpler expressions to find its roots. Simplification may include dividing the entire equation by a common factor to make factoring or other methods easier.

Quadratic Formula and Discriminant

The quadratic formula x = (-b ± √(b² - 4ac)) / 2a provides solutions to any quadratic equation. The discriminant (b² - 4ac) determines the nature of the roots: positive for two real roots, zero for one real root, and negative for complex roots.

Solve each equation in Exercises 83–108 by the method of your choice. 3x2−12x+12=03x^2 - 12x + 12 = 0