Question

In Exercises \(69-72,\) you are tutoring a friend and want to create some quadratic equations that can be solved by factoring. Find a quadratic equation that has the given solutions and explain the procedure you used to obtain the equation. $$8 and - 8$$

Short answer

The quadratic equation with 8 and -8 as solutions is \(x^2 - 64 = 0\).

Step-by-step solution

Analyzing The Roots

Generally, for an equation \(ax^2+bx+c=0\), the solutions \(p\) and \(q\) have the following properties: \(p+q=-b/a\) and \(pq=c/a\). In this case, \(p\) and \(q\) are 8 and -8.

Creating The Equation

The sum of the roots is \(8+ -8=0. \) Therefore, \(b = -0*a=0\). The product of the roots is \(8 * -8 = -64 \) Therefore, \(c= -64* a\).

Resulting equation

Assuming we choose \( a=1 \) for simplicity, the quadratic equation is \( x^2 +0*x -64 = x^2-64 = 0 \), which are the solutions you were looking for.