Question

if one factor of x^3+7kx^2-4kx+12 is (x+3)the value of k is​

Answer 1

Answer:

K=1/5

Step-by-step explanation:

x+3 is factor

therefore, x= -3

substitute the value of x in the equation

-27+63k+12k+12=0

75k=15

k=15/75

k=1/5

Answer 2

Answer :

$\large{\star\:\:\boxed{\bf{k\:=\:\dfrac{1}{5} }}\:\:\star}$

Explanation :

Given :–

• x³ + 7kx² - 4kx + 12 is a Cubic Polynomial .
• (x + 3) is a Factor of x³ + 7kx² - 4kx + 12 .

To Find :–

• The numerical value of k .

Solution :–

⇒g(x) = x + 3 = 0

⇒ x + 3 = 0

⇒ x = (-3)

Now we know that ,

→ p(x) = x³ + 7kx² - 4kx + 12 = 0

Putting the value of x = (-3) :-

→ p(-3) = (-3)³ + 7k(-3)² - 4k(-3) + 12 = 0

→ -27 + 7(9)k + 12k + 12 = 0

→ -27 + 63k + 12k + 12 = 0

→  -15 + 75k = 0

→ 75k = 15

→ k = 15/75

→ k = 1/5

∴ The value of k is 1/5 .