FACTORED FORM OF QUADRATIC EQUATION HOW TO

X 2is the only quantity on the left-hand side of x 2 = 9.

Step 1: Isolate the square variable ( x 2) from other quantities. Take the square root of both sides of the equation.This means that x 2must be the only quantity on the left side, and other quantities must be on the right side. Isolate the square variable ( x 2) from other quantities.Here are the steps to solve quadratic equations by extracting the square root: We usually use this method to solve for x of quadratic equations in the ax 2 = c or ax 2 + c = 0 form.

FACTORED FORM OF QUADRATIC EQUATION HOW TO

Method 1: How To Solve Quadratic Equation by Extracting Square Roots Let us discuss in this section the different methods of solving quadratic equations. Thus, equations a, c, and d are all quadratic equations. Equation d is a quadratic equation in ax 2 = c form.We can transpose -1 to the left side to be in standard form. Equation c is a quadratic equation but not yet in standard form.Equation b is NOT a quadratic equation since the highest exponent of its variable is 3.Equation a is a quadratic equation in factored form.Here are more examples of a quadratic equation in (x + a)(x + b) form or factored form:Įxample: Which of the following are quadratic equations? This is why (x + 2)(x + 3) = 0 is a quadratic equation. Thus, the equation (x + 2)(x + 3) = 0 is actually x2 + 5x + 6 = 0. (x + 2)(x + 3) when multiplied is equal to x2 + 5x + 6. Try to perform the FOIL method on (x + 2)(x + 3) and let’s see what we’ll obtain: You’re probably asking: “But there’s no x 2 in (x + 2)(x + 3) = 0, so why is it a quadratic equation?” In some quadratic equations, the exponent of 2 in the variable can’t be identified unless you perform some computations first.įor instance, (x + 2)(x + 3) = 0 can be considered a quadratic equation. (x + a)(x + b) Form or the Factored Form. You will learn more about this method in the succeeding sections. We usually extract the square root to solve quadratic equations in these forms. In other words, quadratic equations in ax 2 = c form can also appear in the form ax 2 + c = 0. This shows that x 2 = 9 is the same as x 2 – 9 =0. However, if we transpose 9 to the left-hand side of the equation, it will result in the following: Quadratic equations in the form ax 2 = c can also appear in the form of ax 2 + c = 0.įor example, x 2 = 9 is a quadratic equation in ax 2 = c form. As you might have noticed, quadratic equations in this form do not have a linear term or a term with a variable raised to 1. Quadratic equations such as x 2 = 9, 2x 2 = 16, 5x 2 = 10, -x 2 = -1 are in the form ax 2 = c. It is essential to learn about them since there are specific techniques that we can use to solve equations in these forms. Quadratic equations appear in different forms. Not every quadratic equation you will encounter and solve is standard. Later in this review, you’ll learn the importance of determining the values of a, b, and c of a quadratic equation, especially when solving them using the quadratic formula.

Otherwise, we cannot immediately tell the values of a, b, and c.

b = 4 (the numerical coefficient of 4x)Ī quadratic equation’s a, b, and c can be determined only once we have expressed it in standard form ax 2 + bx + c = 0.

a = 2 (the numerical coefficient of 2x 2).

Solution: Since the 2x 2 + 4x – 1 = 0 is already in standard form, then the values of a, b, and c are easy to determine: Therefore, in x 2 + 4x + 4 = 0, the values of a, b, and c are a = 1, b = 4, and c = 4.Įxample: Determine the values of a, b, and c (the real number parts) in 2x 2 + 4x – 1 = 0 In x 2 + 4x + 4 = 0, the constant term is 4. Lastly, the c of a quadratic equation in standard form is the constant term or the term without the x. In x 2 + 4x + 4 = 0, the linear term is 4x and its numerical coefficient is 4. The b of a quadratic equation in standard form is the numerical coefficient of the linear term or the term with x. In x 2 + 4x + 4 = 0, the quadratic term is x 2 and its numerical coefficient is 1. The a of a quadratic equation in standard form is the numerical coefficient of the quadratic term or the term with x 2. We already know that this quadratic equation is in standard form.

Retake a look at this equation: x 2 + 4x + 4 = 0. How To Solve Quadratic Equation by Extracting Square Roots (and Other Techniques) - FilipiKnow

Factored form of quadratic equation