Forming a Quadratic Equation from Given Roots

What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree 2, typically in the form:

$$ax^2 + bx + c = 0$$

where $a$, $b$, and $c$ are constants, and $a \neq 0$.

Forming a Quadratic Equation from Roots

If you know the roots (solutions) of a quadratic equation, you can form the equation itself. Let's say the roots are $p$ and $q$. The quadratic equation can be formed using the formula:

$$(x - p)(x - q) = 0$$

Expanding this, we get:

$$x^2 - (p + q)x + pq = 0$$

Steps to Form a Quadratic Equation

1. Identify the roots: Let's say the roots are $p$ and $q$.
2. Use the formula: Substitute the roots into $(x - p)(x - q) = 0$.
3. Expand: Multiply out the brackets to get the quadratic equation in the form $x^2 - (p + q)x + pq = 0$.

Examples