A quadratic equation is a second-degree equation in an algebraic expression. We have to find the variable x. The variable x has two roots of the quadratic equation. The roots of the equation are represented by α and β. To find the quadratic equation we have to write the given equation in the standard form and then solve the problem. One of the methods to solve the quadratic equation is factoring. Read the entire article to learn how to solve quadratic equation by factoring.
Quadratic Equations by Factoring – Definition & Meaning
In maths, a quadratic equation by factoring is used to find the roots of the equation. Every quadratic equation has two unknown variables of x are α and β. The standard form is ax² + bx + c = 0. If the highest degree is 2 in the given equation then it is called a quadratic equation. The factoring method is nothing but writing the given equation in the simplest form and find the roots of the equation.
Steps for Solving Quadratic Equation by Factoring | How to Solve Quadratic Equations by Factoring?
For solving the quadratic equations by factoring method we have to follow some steps. By following these steps you can simply solve the equation.
Step 1: First write the equation in the standard form of the quadratic equation.
Step 2: Factor the given expression completely.
Step 3: Apply the zero product rule to find the solution.
Step 4: Equate each of the linear equations to 0
Step 5: Solve the values of unknown x.
Step 6: The unknown value of the variable x will be the roots of the equation.
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Solving Quadratic Equations by Factoring Examples with Answers PDF
To solve the quadratic equations the students must have basic knowledge of polynomial expressions. Learn the concept of quadratic equations in-depth and start solving the quadratic equations.
Example 1.
Solve the equation x² -5x + 3 = 0
Solution:
Given the equation x² -5x + 3 = 0
The standard form of the quadratic equation is ax² + bx + c = 0.
x² -5x + 3 = 0
a = 1, b = -5, c = 3
x² -5x + 3 = 0
x² -2x – 3x + 3 = 0
The solution is an imaginary number.
Example 2.
Solve the equation n² = 196
Solution:
Given the equation n² = 196
The standard form of the quadratic equation is ax² + bx + c = 0.
n² – 196 = 0
a = 1, c = -196
n² – 14²= 0
(n + 14)(n – 14) = 0
n + 14 = 0
n = -14
n – 14 = 0
n = 14
The roots of the solution is 14, -14
Example 3.
Solve the equation p² – 7p + 6 = 0
Solution:
Given the equation p² – 7p + 6 = 0
The standard form of the quadratic equation is ax² + bx + c = 0.
a = 1, b = -7, c = 6
p² – 7p + 6 = 0
p² – 1p – 6p + 6 = 0
p(p – 1) -6(p – 1) = 0
(p – 1) (p – 6) = 0
p – 1 = 0
p = 1
p – 6 = 0
p = 6
Example 4.
Solve the equation 3x² – 6x – 10 = 0
Solution:
Given the equation 3x² – 6x – 10 = 0
The standard form of the quadratic equation is ax² + bx + c = 0.
a = 3, b = -6, c = -10
3x² – 6x – 10 = 0
The solution is an imaginary number.
Example 5.
Solve the equation 2x² -5x = -2
Solution:
Given the equation 2x² -5x = -2
The standard form of the quadratic equation is ax² + bx + c = 0.
2x² -5x = -2
2x² -5x + 2 = 0
a = 2, b = -5, x = 2
2x² -5x + 2 = 0
2x² -4x – 1x + 2 = 0
2x(x – 2) -1(x – 2) = 0
(x – 2)(2x – 1) = 0
x – 2 = 0
x = 2
2x – 1 = 0
2x = 1
x = 1/2
Thus the roots of the equation are {2, 1/2}
FAQs on Solving Quadratic Equations by Factoring Method
1. How to factor a quadratic equation?
Factoring the quadratic equation is nothing but breaking the equation into a product of its factors. Expand the equation and simplify according to the factors and equate the linear equation to zero.
2. What are the methods of factoring quadratics?
There are four ways of factoring in the quadratic equation.
i. Splitting the middle term
ii. Using Quadratic formula
iii. Using Algebraic identities
iv. Factoring out the GCD
3. Why called the method of solving quadratic equations by factoring?
To solve the quadratic equation by factoring we use the zero product property. Because we put zero to the split linear equation to find the roots of the equation.