If x - 2 is a factor of x^3 - kx - 12, then the value of k is : 1. 3 2. 2 3. -2 4. -3

By factor theorem, If x - a is a factor of f(x), then f(a) = 0. Given, x - 2 is a factor of x3 - kx - 12 ⇒ x - 2 = 0 ⇒ x = 2. ∴ 23 - 2k - 12 = 0 ⇒ 8 - 2k - 12 = 0 ⇒ -2k - 4 = 0 ⇒ 2k = -4 ⇒ k = = -2. Hence, Option 3 is the correct option.

Mathematics

If x - 2 is a factor of x³ - kx - 12, then the value of k is :
3
2
-2
-3

Factorisation

ICSE 2023

12 Likes

Answer

By factor theorem,

If x - a is a factor of f(x), then f(a) = 0.

Given,

x - 2 is a factor of x³ - kx - 12

⇒ x - 2 = 0

⇒ x = 2.

∴ 2³ - 2k - 12 = 0

⇒ 8 - 2k - 12 = 0

⇒ -2k - 4 = 0

⇒ 2k = -4

⇒ k = $-\dfrac{4}{2}$ = -2.

Hence, Option 3 is the correct option.

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Mathematics

If x - 2 is a factor of x³ - kx - 12, then the value of k is :
3
2
-2
-3

Factorisation

ICSE 2023

Answer

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