Question

The value of k, if x – 1 is the factor of the polynomial x

2 + x +k is

(a) 2 (b) -2 (c) 3 (d) -3​

Answer 1

Hey Pretty Stranger!

• p(x) = 2 + x + k

• g(x) = x - 1

When g(x) = 0

→ x - 1 = 0

→ x = 0 + 1

→ x = 1

Put the value of x = 1 in p(x)

→ 2 + x + k = 0

→ 2 + 1 + k = 0

→ 3 + k = 0

→ 3 - 0 = - k

→ k = 3

$\therefore$ Value of k = 3

Answer 2

Value of k is -2.

Option (b) is correct.

Given:

• If (x-1) is the factor of polynomial ${x}^{2} + x + k$.

To find:

• The value of k is:
• (a) 2
• (b) -2
• (c) 3
• (d) -3

Solution:

Concept/Formula to be used:

• Put the value of x from the factor.
• The polynomial must satisfy, i.e value of polynomial equal to zero.

Step 1:

Find the value of x from the factor.

As,

(x-1) is a factor.

$x - 1 = 0$

or

$\bf x = 1$

Step 2:

Find value of k.

Put x=1 in the polynomial.

$( {1)}^{2} + 1 + k = 0$

or

$1 + 1 + k = 0$

or

$\bf \red{k = - 2}$

Thus,

Value of k is -2.

Option (b) is correct.

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