If x + 1 is a factor of 3x 3 + kx 2 + 7x + 4, then the value of k is 1. -1 2. 0 3. 6 4. 10

By factor theorem, (x - a) is a factor of f(x), if f(a) = 0 . f(x) = 3x 3 + kx 2 + 7x + 4 Since, (x + 1) or (x - (-1)) is a factor of f(x), ∴ f(-1) = 0 ∴ Option 3, is the correct option.

Mathematics

If x + 1 is a factor of 3x³ + kx² + 7x + 4, then the value of k is
-1
0
6
10

Factorisation

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Answer

By factor theorem, (x - a) is a factor of f(x), if f(a) = 0 .

f(x) = 3x³ + kx² + 7x + 4

Since, (x + 1) or (x - (-1)) is a factor of f(x),

∴ f(-1) = 0

$\Rightarrow 3(-1)^3 + k(-1)^2 + 7(-1) + 4 = 0 \\[0.5em] \Rightarrow -3 + k - 7 + 4 = 0 \\[0.5em] \Rightarrow k - 6 = 0 \\[0.5em] k = 6$

∴ Option 3, is the correct option.

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