help with number of real solutions

Question

2x^2-2x+9=0

I don't know what a discriminant is so I do not understand its purpose.

Answer 1

The discriminant is the value under the square-root in the quadratic formula

 

b² - 4ac

 

where:

a = 2

b = -2

c = 9

 

You only have real solutions under this condition

 

b² ≥ 4ac

Answer 2

Given an equation in the form Ax² + Bx + C= 0, the discriminant is

 

B² - 4AC

 

Here, A = 2, B = -2, C= 9

 

B² - 4AC = 4 - 4(2)(9) = 4 - 4(18) = 4 - 72 = -68 < 0

 

This quadratic will have no real solutions since the discriminant is negative