Given the equation 14= x(3x + 19), determine the discriminant and state the number of real and imaginary solutions

Question

Given the equation 14= x(3x + 19), determine the discriminant and state the number of real and imaginary solutions

Answer 1

Dear Tevan,

 

     Hello, let's look at some steps: Your goal is to simplify the quadratic equation, write it in standard quadratic form,

 

and run the following tests on the discriminant.  These tests determine the number of roots and whether they are

 

positive  or negative.

 

b² -4ac is the discriminat taken from radicand inside of the square root of the quadratic quation ( x= [-b +or - √(b2 -4ac)]/ (2a)

 

Here are the tests using the discriminant:   

 

If     b² -4ac > 0 , then discriminant is positive, and there are two real, unique solutions.

 

  

If   b²-4ac< 0,   then discriminant is negative, and there are 2 complex number solutions.

 

 

If   b² -4ac = 0, then there is only one real, repeated root.

 

 

1.  Simplify the equation:  14 = X (3X + 19)                      

 

                                       14=3 X² + 19X

                                     

2. Write equation in standard quadratic form, which is aX² +bX +C=0.

 

                                       0= 3 X² + 19X + -14               Subtract 14 from both sides or add -14 to both sides.

 

3.  Determine the "a, b," and "c" values.

 

a= 3,                    b=19,               c= -14

 

4.  Write the discriminant, and substitute the values for "a, b," and "c."            b²-4ac.

 

     (19)²-4(3)(-14)=361+168=529>0      There will be only two unique, positive solutions, roots.

 

                                                              There are no imagnary or complex root solutions.

 

                                                                         Thank you,

                                                                           Susan C.