Question

The polynomial x² + x + b has (x + 3) as a factor of it.

Statement (1): The value of b is −4 .

Statement (2): (x + 3) is a factor of x² + x + b
⇒ (3)² + 3 + b = 0

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are false.

Explanation:

By factor theorem,

(x − a) is a factor of the polynomial f(x), if the remainder i.e. f(a) = 0.

⇒ x + 3 = 0

⇒ x = −3

Let, f(x) = x² + x + b

Given,

The polynomial x² + x + b has (x + 3) as a factor of it.

⇒ (−3)² + (−3) + b = 0

⇒ 9 − 3 + b = 0

⇒ 6 + b = 0

⇒ b = −6.

∴ Statement 1 is incorrect.

Since,

⇒ (−3)² + (−3) + b = 0

∴ Statement 2 is incorrect.