Question

If ( x+2 ) is the factor of 3x2 – 4kx – 4k , then find the value of k. ​

Answer 1

Given :

• (x+2) is factor of 3x² - 4kx - 4k

To find :

Value of k

Solution :

We are given that ,

• p(x) = 3x² - 4kx - 4k
• g(x) = (x+2)

Now we will put , g(x) = 0 and will find value of x.

➝ x+2 = 0

➝ x = 0-2

➝ x = -2

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Now , for g(x) to be factor of p(x), p(-2) will be zero

➝ p(-2) = 3(-2)² - 4(-2)(k) - 4k

➝ p(-2) = 3(4) + 8k - 4k

➝ 0 = 12 + 8k - 4k

➝ 0 = 12 + 4k

➝ 4k = -12

➝ k = -12/4

➝ k = -3

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ANSWER :

k = -3

Answer 2

Answer:

k = -3

Step-by-step explanation:

p(x) = 3x² – 4kx – 4k

As  ( x+2 ) is the factor of p(x), therefore using factor theorem the remainder should be 0, or p(-2) = 0

( x+2 ) = 0

x = -2

Now, p(x) = 3x² – 4kx – 4k

∴ p(-2) = 3(-2)² – 4k(-2) – 4k

0 = 12 +8k - 4k

0=12 + 4k

4k = -12

k = -12/4 = -3