In the following, determine whether the given quadratic equations have real roots and if so, find the roots:

$x^2-2x+1=0$

Given:

Given quadratic equation is $x^2-2x+1=0$.

To do:

We have to determine whether the given quadratic equation has real roots.

Solution:

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=1, b=-2$ and $c=1$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is

$D=b^2-4ac$.

Therefore,

$D=(-2)^2-4(1)(1)=4-4=0$.

As $D=0$, the given quadratic equation has real and equal roots and the roots are

$x=\frac{-b\pm \sqrt{D}}{2a}$

$x=\frac{-(-2)\pm \sqrt{0}}{2(1)}$ 

$x=\frac{2}{2}$ 

$x=1$

The roots are $1$ and $1$. 

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Updated on: 10-Oct-2022

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