The polynomial p(x) = x² – 2x + 1 has exactly

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Q.
Assertion (A): The polynomial p(x) = x² – 2x + 1 has exactly one zero.

Reason (R): The discriminant of the polynomial is zero.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(1)

The polynomial can be rewritten as (x – 1)², indicating a repeated zero at x = 1.
For p(x) = x² – 2x + 1, we have [a = 1, b = –2, c = 1].
Here, D = b² – 4ac = 4 – 4 = 0.

Solution

Q.
Assertion (A): The polynomial p(x) = x² – 2x + 1 has exactly one zero.

Reason (R): The discriminant of the polynomial is zero.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(1)

The polynomial can be rewritten as (x – 1)², indicating a repeated zero at x = 1.
For p(x) = x² – 2x + 1, we have [a = 1, b = –2, c = 1].
Here, D = b² – 4ac = 4 – 4 = 0.

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Solution

Q. Assertion (A): The polynomial p(x) = x² – 2x + 1 has exactly one zero. Reason (R): The discriminant of the polynomial is zero.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans. (1) The polynomial can be rewritten as (x – 1)², indicating a repeated zero at x = 1. For p(x) = x² – 2x + 1, we have [a = 1, b = –2, c = 1]. Here, D = b² – 4ac = 4 – 4 = 0.

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Q.
Assertion (A): The polynomial p(x) = x² – 2x + 1 has exactly one zero.

Reason (R): The discriminant of the polynomial is zero.

Ans.
(1)

The polynomial can be rewritten as (x – 1)², indicating a repeated zero at x = 1.
For p(x) = x² – 2x + 1, we have [a = 1, b = –2, c = 1].
Here, D = b² – 4ac = 4 – 4 = 0.