Question

Use the discriminant and quadratic fprmula to find the solutions 2x^2-2x+5

Answer 1

The Quadratic Formula:

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

The discriminant is the part of the quadratic formula that's under the square root. (b² - 4ac)
The discriminant tells you how many solutions and what type of solutions (real, non-real) there are.

When the discriminant is 0; there is only one real solution.

`x = (-b )/(2a)`

When the discriminant is a +positive number, There are two real solutions. One for the +√(discriminant) and one for -√(discriminant) in the +/- part of the quadratic formula.

When the discriminant is negative. There are two non-real solutions using the imaginary number i = √(-1)

For your problem: 2x² - 2x + 5
a = 2
b = -2
c = 5

plug these numbers into the quadratic formula:


`x = \frac{-(-2)+/- \sqrt{ (-2)^(2)-4(2)(5) } }{2(2)} \\ \\ x = (2+/- √(4-40) )/(4) \\ \\ x = (2+/- √(-36) )/(4)`

Here you can see the discriminant = -36 is a negative number. There will be 2 non-real solutions.


`x = (2+/- √(-36) )/(4) \\ \\ x = (2+/- √((-1)(36)) )/(4) \\ \\ x = (2+/- i√(36) )/(4) \\ \\ x = (2+/- 6i)/(4) \\ \\ x = (1)/(2)(1 +/- 3i)`