Question

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

Answer 1

x = [ -(-4) +/- sqrt ( (-4)^2 - 4*1*13) ] / 2

x = (4 + sqrt -36) / 2 , (4 - sqrt -36) / 2

x = (4 + 6i) / 2 , (4 - 6i) 2

x = 2 + 3i , 2 - 3i Answer

Answer 2

• Quadratic Formula:
  `x=(-b\pm √(b^2-4ac))/(2a)` , with a = x^2 coefficient, b = x coefficient, and c = constant

With our equation, plug in the values:

`x=(4\pm √((-4)^2-4*1*13))/(2*1)`

Next, solve the exponent and multiplications:

`x=(4\pm √(16-52))/(2)`

Next, solve the subtraction:

`x=(4\pm √(-36))/(2)`

Next, factor out i (i = √-1):

`x=(4\pm √(36)i)/(2)`

Next, solve the square root:

`x=(4\pm 6i)/(2)`

Lastly, divide and your answer is:

`x=2\pm 3i`