Quadratic Equations Mastery Quiz

The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants and $a \neq 0$. An example of a quadratic equation in general form is $2x^2 - 3x + 5 = 0.

The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ can be used to solve a quadratic equation of the form $ax^2 + bx + c = 0$. By substituting the values of $a$, $b$, and $c$ into the quadratic formula, the roots of the equation can be obtained. For example, for the equation $2x^2 - 5x + 3 = 0$, the quadratic formula gives the roots as $x = \frac{5 \pm \sqrt{(-5)^2 - 4(2)(3)}}{2(2)}$.

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the expression $b^2 - 4ac$. It is used to determine the nature of the roots as follows: 1. If the discriminant is greater than 0, the equation has two distinct real roots. 2. If the discriminant is equal to 0, the equation has two identical real roots. 3. If the discriminant is less than 0, the equation has two complex roots.

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