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: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant

With our equation, plug in the values:

$x=\frac{4\pm \sqrt{(-4)^2-4*1*13}}{2*1}$

Next, solve the exponent and multiplications:

$x=\frac{4\pm \sqrt{16-52}}{2}$

Next, solve the subtraction:

$x=\frac{4\pm \sqrt{-36}}{2}$

Next, factor out i (i = √-1):

$x=\frac{4\pm \sqrt{36}i}{2}$

Next, solve the square root:

$x=\frac{4\pm 6i}{2}$

Lastly, divide and your answer is:

$x=2\pm 3i$