Solve each equation by the method of your choice. $3 x^{2} - 7 x + 1 = 0$

검증된 단계별 안내

Identify the given quadratic equation: $3x^2 - 7x + 1 = 0$.

Recall that a quadratic equation in the form $ax^2 + bx + c = 0$ can be solved using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Substitute the coefficients from the equation into the quadratic formula: $a = 3$, $b = -7$, and $c = 1$, so the formula becomes $x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 3 \cdot 1}}{2 \cdot 3}$.

Simplify inside the square root (the discriminant): calculate $b^2 - 4ac = (-7)^2 - 4 \cdot 3 \cdot 1$.

Evaluate the expression under the square root and then compute the two possible values for $x$ by applying the plus and minus signs in the quadratic formula.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

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 typically has two solutions, which can be real or complex numbers.

Factoring and the Zero Product Property

Factoring involves rewriting a quadratic equation as a product of two binomials. The Zero Product Property states that if the product of two factors is zero, then at least one factor must be zero, allowing us to solve for the variable.

Quadratic Formula

The quadratic formula x = (-b ± √(b² - 4ac)) / (2a) provides a method to find the roots of any quadratic equation. It is especially useful when factoring is difficult or impossible, and the discriminant (b² - 4ac) determines the nature of the roots.

Solve each equation by the method of your choice. 3x2−7x+1=03x^2-7x+1 =0