Question

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

x² - 2x + 1 = 0

Answer 1

We have been given, x² - 2x + 1 = 0

Now we also know that for an equation ax² + bx + c = 0, the discriminant is given by the following equation:

D = b² - 4ac

Now, according to the equation given to us, we have,a = 1, b = -2 and c = 1.

Therefore, the discriminant is given as,

D = (-2)² - 4(1)(1)

= 4 - 4

= 0

Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation satisfies this condition, hence it has real and equal roots.

Now, the roots of an equation is given by the following equation,

`x=(-b+-sqrtD)/(2a)`

Therefore, the roots of the equation are given as follows,

`x=(-(-2)+-sqrt0)/(2(1))`

`=2/2`

= 1

Therefore, the roots of the equation are real and equal and its value is 1.