The discriminant is given by b²-4ac. This is what goes under the square root in the quadratic formula. Since we will be taking the square root of this, if the discriminant is less than 0, there are no real roots; you cannot have a real square root of a negative number. If the discriminant is equal to 0, there is 1 real root; the square root of 0 is 0, so the quadratic formula would yield one answer. If the discriminant is greater than 0, there are 2 real roots. This is because taking the square root of a positive number gives a positive and negative result.
b in our equation is -7, a is 3 and c is 4: b²-4ac = (-7)²-4(3)(4) = 49 - 48 = 1
