Question

if x^3 - 4x^2 + 5x - k is completely divisible by x-4 then find the value of k

Answer 1

Answer:

P (x) = x3 - 4x2 + 5x - k.

x - 4 = 0.

x = 4.

P (4) = 0.

Substituting the value of x in P (x) :-

(4)3 - 4 (4)2 + 5 (4) - k = 0.

64 - 64 + 20 - k = 0.

20 - k = 0.

- k = - 20.

k = 20.

Answer 2

As per the data given in the above question.

We have to find the value of k from given condition.

Given,

$x^3 - 4x^2 + 5x - k$

is to be divided by

$x - 4$

Step-by-step explanation:

We have

$p(x) = x^3 - 4x^2 + 5x - k$

$g(x) = x - 4$

Now , put the g(x) is equal to zero , we get

$g(x) = 0$

$x - 4 = 0$

Shift the term to get the value ,

$x = 4$

So, put the value of x and p(x)=0

$p(4) = 0$

$p(4) = x^3 - 4x^2 + 5x - k = 0$

$(4)^3 - 4(4)^2 + 5(4) - k = 0$

$64 - 4 \times 16 + 5 \times 4- k = 0$

$64 - 64 + 20 - k = 0$

$20 - k = 0$

$- k = - 20$

Minus sign cancel out each side ,

Therefore

$k = 20$

The value of k=20 .

Project code #SPJ3