Quadratic Equations

Quadratic Equations A quadratic equation is an equation that takes the form of: $$ax^2 + bx + c = 0$$ where: a is the coefficient of the squared t...

Quadratic Equations

A quadratic equation is an equation that takes the form of:

$ax^2 + bx + c = 0$

where:

a is the coefficient of the squared term
b is the coefficient of the linear term
c is the constant term

Solving a quadratic equation involves finding the roots of the quadratic function represented by the equation. These roots are the x-values where the function's value is equal to zero.

To solve a quadratic equation, we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Example:

Solve the quadratic equation:

$x^2 + 6x + 5 = 0$

Applying the quadratic formula:

$x = \frac{-6 \pm \sqrt{6^2 - 4(1)(5)}}{2(1)}$

$x = \frac{-6 \pm \sqrt{36 - 20}}{2}$

$x = \frac{-6 \pm \sqrt{16}}{2}$

$x = \frac{-6 \pm 4}{2}$

The solutions are:

$x = 3 \text{ and } x = -1$

These values represent the roots of the quadratic equation