The discriminant of an equation tells the nature of the roots of a quadratic equation given that a,b and c are rational numbers.
##D=0##
The discriminant of a quadratic equation ##ax^2+bx+c=0## is given by the formula ##b^2+4ac## of the ;
##x = (-b+-sqrt{b^2-4ac})/(2a)##
The discriminant actually tells you the nature of the roots of a quadratic equation or in other words, the number of x-intercepts, associated with a quadratic equation.
Now we have an equation;
##4x^2−4x+1=0##
Now compare the above equation with quadratic equation ##ax^2+bx+c=0##, we get ##a=4, b=-4 and c = 1##.
Hence the discriminant (D) is given by;
##D = b^2-4ac## ##=> D = (-4)^2 – 4*4*1## ##=> D = 16-16## ##=> D = 0##
Therefore the discriminant of a given equation is 0.
Here the discriminant is equal to 0 i.e. ##b^2-4ac=0##, hence there is only one real root.
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