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QUESTION

What is the discriminant of ##4x^2-4x+1=0## and what does that mean?

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.

Thanks