Question

if x-2 is a factor of x^3-3x+5k then the value of k is
Please anwer it.​

Answer 1

Answer:

$x - 2 = 0 \\ \: \: \: \: \: \: \: \: x = 2$

$p(x) = {x}^{3} - 3x + 5k$

$p(2) = ( {2})^{3} - 3(2) + 5k \\ \: \: \: \: \: \: \: \: \: =8 - 6 + 5k \\ \: \: \: \: \: \: \: \: \: = 2 + 5k \\ \: \: \: 5k= ( - 2) \\ \: \: \: \: \: k = \frac{( - 2)}{5}$

Answer 2

ANSWER :–

K = - (⅖)

EXPLANATION :–

GIVEN :–

A polynomial x³ - 3x + 5k have a factor (x - 2).

TO FIND :–

Value of 'k'.

SOLUTION :–

• If (x - 2) is a factor then x = 2 will satisfy the polynomial.

• Let the polynomial be p(x) = x³ - 3x + 5k

• Now put x = 2 –

=> p(2) = 0

=> (2)³ - 3(2) + 5k =0

=> 8 - 6 + 5k = 0

=> 2 + 5k = 0

=> 5k = -2

=> k = -(⅖)

Extra information :–

☞ Every factor of polynomial always will satisfy the polynomial.