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