Question

Use the quadratic formula to solve for the roots of the following equation. x2 - 4x + 13 = 0

Answer 1

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

Step-by-step explanation:

• Step 1: Given equation is x² - 4x + 13 = 0. Here a = 1, b = -4, c = 13. Use the quadratic formula to find the roots.

x = (-b ±√b²-4ac)/2a

⇒ x = (4±√16 - 4×1×13)/2

⇒ x = (4 ± √-36)2

⇒ x = 4 ±6i/2 = 2 + 3i, 2 - 3i

Answer 2

Answer:

No solution in R (if you consider complex numbers then the other answer is correct)

Step-by-step explanation:

quadratic formula:

x1 = $\frac{-b + \sqrt{b^2 - 4ac} }{2a}$

x2 = $\frac{-b - \sqrt{b^2 - 4ac} }{2a}$

​calculate the discriminant b²-4ac first

(-4)² - 4*13 = 16 - 52 = - 36

square root of a negative number does not exist in R and a discriminant < 0 indicates no solutions in R