Free thyroxine (free T4) tests are used to help evaluate thyroid function and diagnose thyroid diseases, including hyperthyroidism and hypothyroidism, usually after discovering that the thyroid stimulating hormone (TSH) level is abnormal. T4 and another hormone called triiodothyronine (T3) are produced by the thyroid gland.
[When the determinant of a matrix is nonzero, linear system it represents is linearly independent]. When the determinant of a matrix is zero, it rows are linearly dependent vectors, and its columns are linearly dependent vectors.
The discriminant tells us there are two roots when positive, one root when zero, and no roots when negative. #b^2-4ac = (-8)^2-4*3*1 = 52# is positive, so there are two roots. The discriminant is just part of the quadratic equation. The quadratic equation gives us the exact real number roots of any equation in the form #ax^2+bx+c=0#. The quadratic equation is #x = (-b \pm sqrt(b^2-4ac))/(2a)#, where #\pm# means that we have two values, one using #+# (addition) and one using #-# (subtraction).