Question

describe the nature of the roots for this equation, x^2-2x+1=0

Answer 1

Use the discrimant to determine the nature of the roots
Here's the formula of the discriminant from the equation ax²+bx+c = 0
D = b² - 4ac

If the discriminant is greater than 0, the quadratic equation has 2 real different roots
If the discriminant is equal to 0, the quadratic equation has only one real root.
If the discriminant is less than 0, the quadratic equation doesn't have real root.

Find the discriminant of the equation x² - 2x + 1 = 0
D = b² - 4ac
D = (-2)² - 4(1)(1)
D = 4 - 4
D = 0
The equation has only one real root.

Answer 2

The equation has only one real root.

Given that,

Equation; $\rm x^2-2x+1=0$

We have to determine,

The nature of the roots.

According to the question,

The nature of the roots of the given equation is determined by using the following formula;

$\rm Discriminate = b^2-4ac$

Equation; $\rm x^2-2x+1=0$

The value of a = 1, b =-2, c=1.

Substitute all the values in the formula;

$\rm Discriminate = b^2-4ac\\\\\rm Discriminate =(-2)^2-4\times 1 \times 1\\\\\rm Discriminate =4-4\\\\\rm Discriminate =0$

Hence, The equation has only one real root.

To know more about the Quadratic equation click the link given below.

https://brainly.com/question/12895249