Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0

Question

  x 2 – 4x + 13 = 0

Answer 1

From the standard form ax² + bx + c = 0  ; a = 1; b = -4 ; c = 13

 

The quadratic formula is x = (-b +-(b² - 4ac)^1/2)/2a

 

x = (4 +-(16 - 52)^1/2)/2

 

x = (4 +-(-36)^1/2)/2

 

using the imaginary quantity i = (-1)^1/2

 

x = (4 +- 6i)/2

 

The two roots are: 2 + 3i   and   2 - 3i

Answer 2

The quadratic formula is:

 

       -b ± √(b²-4ac)

x = ---------------------

              2a

 

In your problem

 

x2 - 4x + 13 = 0

 

a = 1, b = -4, c = 13.  Plug those values into the quadratic formula and compute the answers.  The expression under the radical (the discriminant) is negative, so you will get roots that are complex numbers.  There will be two roots.