What is a quadratic equation? How can you solve a quadratic equation by the factorization method?

An algebraic expression in the form of ax² + bx + c = 0 is called a quadratic equation. It has a degree value of 2.

Answer: An algebraic expression in the form of ax² + bx + c = 0 is called a quadratic equation. We can solve a quadratic equation by the factorization method by determining the factors of the equation.

Let's understand how to determine the factors of a quadratic equation in detail.

Explanation:

The solution to a quadratic equation can be found using different methods such as completing the squares, quadratic formula, factorization, etc.

Following are the steps to solve an equation using the factorization method.

Step 1: Convert the quadratic equation in standard form.

Let ax² + bx + c = 0 is standard form of the equation.

Step 2: Split the middle term that is coefficient of x as a sum or difference of factors of a × c.

⇒ Let b₁ and b₂ be the sum of factors.

⇒ Product of the factors be ( a × c ) = ( b₁ + b₂ ) sum of the factors.

⇒ ax² + (b₁ + b₂) x + c= 0

Step 3: By taking out the common factors, we get the desired factors.

Let us solve the quadratic equation x² - x - 6 = 0

⇒ x² - x - 6 = 0

⇒ x² - 3x + 2x - 6 = 0

⇒ x (x - 3) + 2(x - 3) = 0

⇒ (x - 3) (x + 2) = 0

You can use Cuemath's Quadratic Factoring Calculator to find the factors of the quadratic equation.

Thus, we can solve the quadratic equation by using the factorization method.