To find the discriminant of a quadratic equation like y^(2)+9y+1=0, we can use the formula specified as b^2-4ac, where "a" is the coefficient of y^2, "b" is the coefficient of y, and "c" is the constant.
In this equation, a = 1, b = 9, and c = 1.
We are going to substitute these values into our formula:
* The square of b is 9^2 which equals to 81.
* 4 times a times c equals to 4*1*1 which is 4.
Subtracting 4 from 81 as per our formula, the discriminant comes out to be 81 - 4 = 77.
So, the discriminant of y^(2)+9y+1=0 is 77.