Question

the nature of the roots of the quadratic equation x²-2x+1=0
a)real and equal
b)real, rational and distinct
c)real, irrational and distinct
d)complex​

Answer 1

Answer:

real and equal, with zeros are 1 , 1

Answer 2

Answer:

Given :-

• x² - 2x + 1 = 0

To Find :-

• What is the nature of the roots of the quadratic equation.

Formula Used :-

$\clubsuit$ Discriminant Formula :

$\mapsto \sf\boxed{\bold{\pink{Discriminant\: (D) =\: b^2 - 4ac}}}$

Solution :-

Given Equation :

$\bigstar\: \sf\bold{\purple{x^2 - 2x + 1 =\: 0}}$

where,

• a = 1
• b = - 2
• c = 1

According to the question by using the formula we get,

$\longrightarrow \sf Discriminant\: (D) =\: b^2 - 4ac$

$\longrightarrow \sf Discriminant\: (D) =\: (- 2)^2 - 4(1)(1)$

$\longrightarrow \sf Discriminant\: (D)\: =\: (- 2)(- 2) - 4 \times 1 \times 1$

$\longrightarrow \sf Discriminant\: (D) =\: 4 - 4 \times 1$

$\longrightarrow \sf Discriminant\: (D) =\: 4 - 4$

$\longrightarrow \sf\bold{\red{ Discriminant\: (D) =\: 0}}$

$\therefore$ The discriminant of the quadratic equation is 0.

And, the nature of the roots the quadratic equation is real and equal.

Hence, the correct options is option no (a) real and equal.