Question

if a polynomial x*4-3x*3-6x*2+kx -16 is exactly divisible by x*2-3x+2 then find value of k

Answer 1

Here is your answer
k = 24
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Answer 2

Answer:

The value of k is 24.

Step-by-step explanation:

Let,

$f(x)=x^4-3x^3-6x^2+kx -16$

Given,

f(x) is exactly divisible by  $x^2-3x+2$

That is,

f(x) is a multiple of $x^2-3x+2$

Also,

$x^2-3x+2=x^2-2x-x+2=x(x-2)-1(x-2)=(x-1)(x-2)$

⇒ f(x)  is a multiple of $(x-1)(x-2)$

⇒ f(x) is a multiple of (x-1),

⇒ x = 1 is one of the zeroes of f(x)

⇒ f(1) = 0

⇒ $(1)^4-3(1)^3-6(1)^2+k(1) -16=0$

⇒ $1-3-6+k -16=0\implies k-24=0\implies k = 24$

Hence, The value of k is 24.