What Is A Double Solution

SOLVING QUADRATIC EQUATIONS

Notation:

• A quadratic equation is a polynomial equation of degree 2.
• The ''U'' shaped graph of a quadratic is called a parabola.
• A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.
• There are several methods y'all can use to solve a quadratic equation:
  1. Factoring
  2. Completing the Square
  3. Quadratic Formula
  4. Graphing
• All methods start with setting the equation equal to zero.

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Solve for x in the following equation.

Example ane:

Set the equation equal to naught by subtracting 3 x and vii from both sides of the equation.

Method ane: Factoring

The left side of the equation is not easily factored, so we will not use this method.

Method 2: Completing the Square

Decrease 15 from both sides of the equation .

Add together to both sides of the equation:

Gene the left side and simplify the right side :

Accept the square root of both sides of the equation:

Add to both sides of the equation:

and

Method 3: Quadratic Formula

The quadratic formula is

In the equation ,a is the coefficient of the term, b is the coefficient of the x term, and c is the constant. Simply insert 1 for a, -3 for b, and xv for c in the quadratic formula and simplify.

and

Method 4: Graphing

Graph y= the left side of the equation or and graph y= the correct side of the equation or y=0. The graph of y=0 is nothing more than the x-axis. So what you lot will exist looking for is where the graph of crosses the x-axis. Another way of saying this is that the 10-intercepts are the solutions to this equation.

Yous can see from the graph that there are no x-intercepts. This means that at that place are no real answers; the solution are two imaginary numbers.

The answers are and These answers may or may not be solutions to the original equations. You must verify that these answers are solutions.

Cheque these answers in the original equation.

Check the solution past substituting in the original equation for x. If the left side of the equation equals the correct side of the equation after the commutation, you have found the right answer.

• Left Side:

  
  

  
  

  
  

  
  

• Correct Side:

Since the left side of the original equation is equal to the correct side of the original equation afterwards nosotros substitute the value for ten, and so is a solution.

Check the solution by substituting in the original equation for x. If the left side of the equation equals the correct side of the equation afterward the substitution, y'all have found the correct answer.

• Left Side:

  
  

  
  

  
  

  
  

• Correct Side:

  
  

  
  

Since the left side of the original equation is equal to the right side of the original equation afterwards we substitute the value for x, then is a solution.

The solutions to the equation are and

Annotate: You tin use the solutions to cistron the original equation.

For example, since ,then

Since , then

Since the product

then we can say that

This means that and are factors of

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If you would similar to work another example, click on Example.

If you lot would like to examination yourself by working some problems similar to this example, click on Trouble.

If you would similar to go back to the equation table of contents, click on Contents.

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Author: Nancy Marcus

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What Is A Double Solution,

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