The equation x^2-3 x+a=0 has two roots. One root of the...

The equation $x^{2}-3 x+a=0$ has two roots. One root of the equation is $2 .$ What is the other root?
$$
\begin{array}{lllll}{\text { A. }-2} & {\text { B. }-1} & {\text { C. } 1} & {\text { D. } 3}\end{array}
$$

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Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a, b, and c are constants and a ? 0. Understanding quadratic equations is essential because they represent a fundamental class of equations with unique properties and solution methods.

Substitution Method

The substitution method involves replacing a variable with a known value in an equation to simplify it or to solve for an unknown coefficient or variable. In problems where one root of a polynomial is given, substitution allows determination of unknown parameters by setting the equation equal to zero.

Vieta's Formulas

Vieta's formulas provide relationships between the roots of a polynomial and its coefficients. For a quadratic equation ax² + bx + c = 0, the sum of the roots equals -b/a and the product equals c/a. This connection can be used to find missing roots or to verify solutions.

Factoring

Factoring involves rewriting a polynomial as the product of its factors, which are often simpler linear expressions. In the context of quadratic equations, factoring is a useful tool when the equation can be broken down into two binomials, thereby revealing the roots directly.

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