Question

If x+1 is a factor of kx^4+4x^3-12x^2+4k .find value of k

Answer 1

Answer:

The value of k is 16/5.

Step-by-step explanation:

Given polynomial: p(x) = kx⁴ + 4x³ - 12x² + 4k

g(x) = x + 1

Zeroes of g(x) = -1 (Because x + 1 = 0, x = -1)

Put x = -1 in p(x).

p(-1) = k(-1)⁴ + 4(-1)³ - 12(-1)² + 4k = k(1) + 4(-1) - 12(1) + 4k = k -4 -12 + 4k = 5k - 16

But, since g(x) is a factor of p(x), p(-1) = 0.

Thus, 5k - 16 = 0

or, 5k = 16 or, k = 16/5

Hence, the value of k is 16/5.

Answer 2

$\underline{\underline{\bold{Question:}}}$

If ( x + 1 ) is a factor of kx⁴ +4x³ - 12x² + 4k . Find the value of k.

$\underline{\bold{Solution:}}$

Given :

• ( x + 1 ) is a factor .

So

$\implies{\bold{x+1=0}}\\\\\\\boxed{\textsf{\bold{ x = -1.}}}\\\\\\\underline{\bold{\textsf{Put the value of x,}}}\\\\\\\implies{\bold{kx^{4}+4x^3-12x^2+4k=0\qquad(Factor\:theorem). }}\\\\\\\implies{\bold{k(-1)^4+4(-1)^3-12(-1)^2+4k=0}}\\\\\\\implies{\bold{k-4-12+4k=0}}\\\\\\\implies{\bold{5k=16}}\\\\\\\implies{\bold{k=\dfrac{16}{5}=3.2}}\\\\\\\\\boxed{\boxed{\bold{k=3.2}}}$