Find the solutions of the equation, 1/2x² - x + 5 = 0.

Solution:

Given equation is 1/2x² - x + 5 = 0

Multiply the given equation by 2

x² - 2x + 10 = 0

We know that, if quadratic equation is of the form ax² + bx + c = 0 then its solutions are,

\(x = \frac{-b \pm \sqrt{b^{2} -4ac}}{2a}\)

Here a = 1, b = -2, c = 10

x = {-(-2) ± √[(-2)² - 4(1)(10)]} / 2(1)

x = [2 ± √(-36)] / 2

x = [2 ± 6 i] / 2

x = 1± 3 i

Thus we can conclude that the given quadratic equation does not have a real solution.

Find the solutions of the equation, 1/2x² - x + 5 = 0.

Summary:

The given equation, 1/2x² - x + 5 = 0 does not have a real solution.