Mathematics
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.
option
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.
Factorisation
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Answer
Both the statements are false.
Reason
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.
Hence, option 2 is the correct option.
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Related Questions
Two polynomials x36 - 3x35 and x - 3.
Assertion (A) : If x - 3 is a factor of x36 - 3x35, the remainder is zero.
Reason (R) : The polynomial x - a is factor of polynomial p(x) = x36 - ax35, if p(a) = 0
options
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
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The polynomial 3x3 + 8x2 - 15x + k and one of its factors as (x - 1).
Assertion (A) : The value of k = 4.
Reason (R) : x - 1 = 0 ⇒ x = 1.
∴ 3.(1)3 + 8.(1)2 - 15 x (1) + k = 0
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A is true, R is false.
A is false, R is true.
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A polynomial x4 - 13x2 + 36.
Statement 1: x - 2 is a factor of x4 - 13x2 + 36.
Statement 2: (2)4 - 13 x (2)2 + 36 = 0.
option
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Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
When x3 + 3x2 - mx + 4 is divided by x - 2, the remainder is m + 3. Find the value of m.