Question

The value of k for which which x minus 1 is a factor of PX is equal to x square minus x + k

Answer 1

Question :

The value of k for which (x - 1) is a factor of p(x) = x² - x + k

Answer :

$\boxed{=>k=0}$

Given :

(x - 1) is a factor of the polynomial, p(x) = x² - x + k

To find :

the value of k

Solution :

 

  (x - 1) is a factor of x² - x + k

∴ The remainder when x² - x + k is divided by (x - 1) is 0

=> (x - 1) is a factor

      x - 1 = 0

       x = +1

Put x = 1,

    and since the remainder is 0, p(1) = 0

p(x) = x² - x + k

p(1) = 1² - 1 + k =0

        1 - 1 + k = 0

          0 + k = 0

               k = 0

∴ The value of k is "0"

 

Answer 2

Step-by-step explanation:

The value of k for which (x - 1) is a factor of p(x) = x² - x + k

Answer :

$\boxed{= > k=0} </p><p>=>k=0$

Given :

(x - 1) is a factor of the polynomial, p(x) = x² - x + k

(x - 1) is a factor of the polynomial, p(x) = x² - x + kTo find :

(x - 1) is a factor of the polynomial, p(x) = x² - x + kTo find :the value of k

Solution :

(x - 1) is a factor of x² - x + k

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1,

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0p(x) = x² - x + k

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0p(x) = x² - x + kp(1) = 1² - 1 + k =0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0p(x) = x² - x + kp(1) = 1² - 1 + k =0 1 - 1 + k = 0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0p(x) = x² - x + kp(1) = 1² - 1 + k =0 1 - 1 + k = 0 0 + k = 0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0p(x) = x² - x + kp(1) = 1² - 1 + k =0 1 - 1 + k = 0 0 + k = 0 k = 0

(x - 1) is a factor of x² - x + k∴ The remainder when x² - x + k is divided by (x - 1) is 0=> (x - 1) is a factor x - 1 = 0 x = +1Put x = 1, and since the remainder is 0, p(1) = 0p(x) = x² - x + kp(1) = 1² - 1 + k =0 1 - 1 + k = 0 0 + k = 0 k = 0∴ The value of k is "0"