Table of Contents
What is Quadratic Equation?
A quadratic equation is an equation in the form ax2+bx+c=0, where a, b, and c are constants. The equation has a unique solution if and only if the discriminant, b2-4ac, is equal to or greater than zero.
Different Ways for Solving of Quadratic Equation:
There are four methods of solving quadratic equations:
The Quadratic Formula
factorization
completing the square
the square root method
The Quadratic Formula
The quadratic equation can be solved using the quadratic formula, which is:
where:
a is the coefficient of the x2 term
b is the coefficient of the x term
c is the constant term
The quadratic equation can also be solved using the factoring method.
factorization
The factoring method can be used to solve a quadratic equation if the equation can be factored into two linear equations.
completing the square
The completing the square method can be used to solve a quadratic equation if the equation can be rewritten as a perfect square.
square root method
The square root method can be used to solve a quadratic equation if the equation can be rewritten as a square root.
A quadratic equation is an equation in the form ax^2+bx+c=0. Factoring a quadratic equation is the process of rewriting the equation in the form (x-h)^2=k, where h is the x-intercept and k is the y-intercept. There are three ways to solve a quadratic equation: using the quadratic formula, completing the square, or using the factoring method.
The quadratic formula is a formula that can be used to solve any quadratic equation. The formula is:
x= (-b +- sqrt(b^2-4ac))/(2a)
Completing the square is a method that can be used to solve a quadratic equation when the coefficient of x^2 is 1. The method involves rewriting the equation in the form x^2+bx+c=0, and then completing the square.
The factoring method is a method that can be used to solve a quadratic equation when the coefficient of x^2 is not 1. The method involves factoring the equation into the form (x-h)^2=k, and then solving for x.
Here is an example of how to use the factoring method to solve a quadratic equation:
x^2-4x+3=0
The equation can be rewritten in the form (x-h)^2=k, where h is the x-intercept and k is the y-intercept.
(x-3)^2=0
The equation can be solved by using the quadratic formula.
x=3
Here is an example of how to use the completing the square method to solve a quadratic equation:
x^2+6x+9=0
The equation can be rewritten in the form x^2+bx+c=0.
x^2+6x+9-9=0
The equation can be completed by adding 9 to each side.
x^2+6x=0
The equation can be solved by using the quadratic formula.
x=0
A quadratic equation is an equation in the form ax2+bx+c=0, where a, b, and c are real numbers and a≠0. Factoring a quadratic equation is the process of rewriting the equation in the form of a product of two binomial expressions.
There are three methods for factoring quadratic equations: the quadratic formula, completing the square, and using the Quadratic Formula. The Quadratic Formula is the most general method and can be used to solve any quadratic equation.
The Quadratic Formula is
x=−b±√b2−4ac
To use the Quadratic Formula, you need to know the values of a, b, and c. There are three steps to using the Quadratic Formula:
1. Substitute the values of a, b, and c into the Quadratic Formula.
2. Solve for x.
3. Check your answer.
Here is an example of how to use the Quadratic Formula:
x2−5x+6=0
a=1
b=−5
c=6
x=−b±√b2−4ac
x=− (−5)±√ (−5)2−4(1)(6)
x=5±√25
x=5±5
x=10±5
The Quadratic Formula gives two answers, 10±5. To find the solutions, you need to solve each equation. 10±5=5±5, so there are two solutions, 5±5.
Here is another example:
x2+10x+25=0
a=1
b=10
c=25
x=−b±√b2−4ac
x=− (−10)±√ (−10)2−4(1)(25)
x=10±√100
x=10±10
x=20±10
The Quadratic Formula gives two answers, 20±10. To find the solutions, you need to solve each equation. 20±10=10±10, so there are two solutions, 10±10.
