Question

The nature of the roots of the quadratic equation x²-2x+1=0 are


A. real and equal

B. real, rational and distinct

C. real, irrational and distinct

D. complex

like and follow​

Answer 1

EXPLANATION.

Nature of the roots of the quadratic equation.

⇒ x² - 2x + 1 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

⇒ D = (-2)² - 4(1)(1).

⇒ D = 4 - 4.

⇒ D = 0.

Roots are real and equal.

Option [A] is correct answer.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

Given :-

x² - 2x + 1

To Find :-

Roots

Solution :-

We know that

D = b² - 4ac

Here

a = 1

b = -2

c = 1

On putting value we get

D = -2² + 4 × 1 × 1

D = (-2 × -2) + 4 × 1

D = 4 + (-4)

D = 4 - 4

D = 0

As we know that

If D = 0, Then roots are real and equal

Check :-

x² - 2x + 1

Spilt the midle term

x² - (x + x) + 1

x² - x - x + 1

x(x - 1) - 1(x - 1)

(x - 1)(x - 1)

We may see that the roots are same. Therefore, Option A is correct