Question

What is the value of the discriminant of f ?
F(x) = 3x^2 + 12x + 5

Answer 1

The answer is F(x) = 3(x+2)^2-7

Answer 2

The usual discriminant is d=b²-4ac

d = (12)² - 4(3)(5) = 144 - 60 = 84

Answer: 84

When we have an even b like this we can get 1/4 of the usual discriminant with (b/2)²-ac = 6² - (3)(5) = 36 - 15 = 21. That's a bit easier to calculate and usually just as good.