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

y2 - 5y - 3 = 0

double root

real and rational root

real and irrational root

non-real root

The coefficients are a=1, b=-5, c=-3, so the discriminant b²-4ac is

... (-5)²-4(1)(-3) = 25+12 = 37

The discriminant is positive, but not a square. The two distinct roots are each real and irrational.

to complete this square you have to rotate about the origin 270 degrees clockwise.