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

1 Answer
Jul 24, 2015

Answer:

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#

Explanation:

The discriminant of a quadratic equation #ax^2+bx+c=0# is given by the formula #b^2+4ac# of the quadratic formula;

#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