Question

(x-3) is a factor of polynomial x^3-3x^2+5x+k then the value of k is​

Answer 1

Answer:

k=-15

Step-by-step explanation:

x-3=0

x=3

By substituting the x value in the equation

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

27 - 27 + 15 +k = 0

15 + k=0

k = -15

Answer 2

QUESTION :-

If (x - 3) is a Factor of the Polynomial $x^3 - 3x^2 + 5x + k$, then the Value of k is

SOLUTION :-

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

g (x) = x - 3

Then,

g (x) = 0 => x - 3 = 0 => ∴ x = 3

By Factor Theorem, (x - 3) will be a Factor of p (x), if p (3) = 0 :

Now,

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

$\Rightarrow 27 - 3(9) + 15 + k = 0\\\\\Rightarrow 27 - 27 + 15 + k = 0\\\\\Rightarrow 15 + k = 0\\\\Therefore,\:\bold k = 0 - 15 = \bold {(-15)}$

Hence, the Required Value of k is (-15)