Quadratic Equations Basics
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Questions and Answers

What are the solutions of a quadratic equation and what are they called?

The values of $x$ that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side.

In the standard form of a quadratic equation $ax^2 + bx + c = 0$, what do the coefficients $a$, $b$, and $c$ represent?

The coefficients $a$, $b$, and $c$ represent known numbers, where $a eq 0$. $a$ is the quadratic coefficient, $b$ is the linear coefficient, and $c$ is the constant coefficient or free term.

How many solutions does a quadratic equation have?

A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root.

What is the quadratic formula and how is it related to the solutions of a quadratic equation?

<p>The quadratic formula expresses the solutions in terms of $a$, $b$, and $c$. It is used to find the roots of a quadratic equation, which are the values of $x$ that satisfy the equation.</p> Signup and view all the answers

What types of solutions can a quadratic equation with real coefficients have?

<p>If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other.</p> Signup and view all the answers

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