Solve each quadratic equation using the zero-factor property. See Example 5. x² - 5x + 6 = 0

검증된 단계별 안내

Start with the quadratic equation given: \(x^{2} - 5x + 6 = 0\).

Factor the quadratic expression on the left side. Look for two numbers that multiply to \(6\) (the constant term) and add up to \(-5\) (the coefficient of \(x\)).

Write the factored form as \((x - a)(x - b) = 0\), where \(a\) and \(b\) are the numbers found in the previous step.

Apply the zero-factor property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero: \(x - a = 0\) and \(x - b = 0\).

Solve each equation for \(x\) to find the solutions to the quadratic equation.

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주요 개념

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

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, generally written as ax² + bx + c = 0. It represents a parabola when graphed and can have zero, one, or two real solutions depending on the discriminant.

Factoring Quadratic Expressions

Factoring involves rewriting a quadratic expression as a product of two binomials. For example, x² - 5x + 6 factors into (x - 2)(x - 3). This step is essential to apply the zero-factor property to find the roots.

Zero-Factor Property

The zero-factor property states that if the product of two factors equals zero, then at least one of the factors must be zero. This principle allows solving equations like (x - 2)(x - 3) = 0 by setting each factor equal to zero.