Question

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

Answer 1

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