The polynomial s(x) = x³

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Q.
Assertion (A): The polynomial s(x) = x³ – x has three real zeros.

Reason (R): The polynomial can be factored into x(x – 1)(x + 1), which means its 3 zeros are –1, 0, and 1.

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 zeros of s(x) derived from its factored form x(x – 1)(x + 1) are x = 0, 1, and –1, which indeed are three real zeros.
Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Solution

Q.
Assertion (A): The polynomial s(x) = x³ – x has three real zeros.

Reason (R): The polynomial can be factored into x(x – 1)(x + 1), which means its 3 zeros are –1, 0, and 1.

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 zeros of s(x) derived from its factored form x(x – 1)(x + 1) are x = 0, 1, and –1, which indeed are three real zeros.
Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

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Solution

Q. Assertion (A): The polynomial s(x) = x³ – x has three real zeros. Reason (R): The polynomial can be factored into x(x – 1)(x + 1), which means its 3 zeros are –1, 0, and 1.

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 zeros of s(x) derived from its factored form x(x – 1)(x + 1) are x = 0, 1, and –1, which indeed are three real zeros. Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Want Us to Email you About Special Offers & Updates?

Q.
Assertion (A): The polynomial s(x) = x³ – x has three real zeros.

Reason (R): The polynomial can be factored into x(x – 1)(x + 1), which means its 3 zeros are –1, 0, and 1.

Ans.
(1)

The zeros of s(x) derived from its factored form x(x – 1)(x + 1) are x = 0, 1, and –1, which indeed are three real zeros.
Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).