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

1 Answer
Jul 24, 2015

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