Question

If the factor of 3x⁴ - (a + 2)x³ - x² - 4 is (x - 2), then the value of a is-

A. 5

B. -1

C. 3

D. 4

1. D
2. A
3. C
4. B

Answer 1

Correct Answer - Option 3 : C

Given:

f(x) = 3x4 - (a + 2)x3 - x2 - 4 

p(x) = (x - 2)

Concept used:

Using concept of factor theorem,

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

calculation:

(x - 2) is factor of f(x) = 3x4 - (a + 2)x3 - x2 - 4 

using factor theorem,

f(2) = 0

⇒ 3 × 24 - (a + 2) × 23 - 22 - 4 = 0

⇒ 3 × 16 - (a + 2) × 8 - 4 - 4 = 0

⇒ 48 - 8a - 16 - 4 - 4 = 0

⇒ -8a = -24

⇒ a = 3

∴ The value of a is 3.