Write a quadratic equation in general form whose solution set is {- 3, 5}.

Key Concepts

Quadratic Equation

A quadratic equation is a polynomial equation of degree two, typically expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The solutions to this equation, known as the roots, can be found using various methods such as factoring, completing the square, or the quadratic formula.

Roots of a Quadratic Equation

The roots of a quadratic equation are the values of x that satisfy the equation, meaning they make the equation equal to zero. For a quadratic with roots r₁ and r₂, the equation can be expressed in factored form as a(x - r₁)(x - r₂) = 0. In this case, the roots are given as -3 and 5.

General Form of a Quadratic Equation

The general form of a quadratic equation is represented as ax² + bx + c = 0. To write a quadratic equation in this form given its roots, one can use the factored form and expand it. For roots -3 and 5, the equation can be derived by multiplying the factors (x + 3)(x - 5) and then rearranging it into the general form.