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

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 $a {x}^{2} + b x + c = 0$ is given by the formula ${b}^{2} + 4 a c$ of the quadratic formula;

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

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 $a {x}^{2} + b x + c = 0$, we get $a = 4 , b = - 4 \mathmr{and} c = 1$.

Hence the discriminant (D) is given by;

$D = {b}^{2} - 4 a c$
$\implies D = {\left(- 4\right)}^{2} - 4 \cdot 4 \cdot 1$
$\implies D = 16 - 16$
$\implies D = 0$

Therefore the discriminant of a given equation is 0.

Here the discriminant is equal to 0 i.e. ${b}^{2} - 4 a c = 0$, hence there is only one real root.

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