Use the discriminant to determine the nature of the roots of the following equation.

y2 - 5y - 3 = 0

Discussion

The discriminate is b^2 - 4*a*c

The general equation for a quadratic is ax^2 + bx + c

In this equation's case

a = 1

b = - 5

c = - 3

Solve

(-5) ^2 - 4 * (1) * (-3)

25 - (-12)

25 + 12

37

Note

Since the discriminate is > 0, the roots are real and different. The roots do exist and there are 2 of them.