Use the quadratic formula to solve the following quadratic equations.

Question

1.Use the quadratic formula to solve the following quadratic equations.

 

i.x^2-4x+13=0

 

ii.4x^2+16x+25=0

Answer 1

Here are some steps to follow to answer the first equation.  The second can be done in the same way as the first one.

 

1.  Write the standard form for Quadratic Equations.         aX²  + bX   + C = 0

 

2.  Write the equation, and determine the values for a, b,  and c .

 

1X²  -4x +13 = 0                        a= 1  ,   b= -4 ,     c= 13

 

3.  Write the Quadratic Formula every time you work a problem like this one: 

 

X=  - (b)   +/-    √( (b)² -  4ac) / 2a           Note:  Everything on top( the numerator) is being divided by twice a.

                     

 

4.  Substitute a, b, and c values into the Quadratic Equation.  

 

X =  -(-4)   +/-  √(( -4)² -4* 1*13)/ 2(1)      =  4  +/-  √(16-52) / 2    =    4 +/-  √(-36)/2

 

5.  You need to simplify the negative number in the radical before completing the problem:  √-36  =  √(36* -1)

 

     √36    * √-1                  Note:  √-1  is an imaginary number       i=√-1

 

    √36 = 6                Therefore,      6√-1    =    √-36

 

6.    +/-  means that you have to write two separate equations.  You have two roots.

 

     X=  (4 +  6√i ) /  2                and    X=  (4 - 6√i )/ 2               

 

You have two complex roots(answers for X) made up of real and imaginary numbers.

 

If you have any questions or problems, please ask me further.   Thank you.