Question

If x +1 is a factor of the polynomial 2

square+ kx + 1 , then the value of k is.​

Answer 1

Correct Question :-

If x + 1 is a factor of the polynomial 2x^2 + kx + 1 .Find the value of k.

Answer :-

3

Explanation :-

Given :

Polynomial => 2x^2 + kx + 1

To Find :

The value of k

Solution :

x + 1 = 0

⇒ x = 1

Let the given polynomial be =>

$\sf{}p(x)= 2x^2 + kx + 1$

[putting x = -1]

$\sf{}p(-1)= 2(-1)^2 + k(-1) + 1$

$\sf{}\Rightarrow 0= 2(1) -k + 1$

$\sf{}\Rightarrow 0= 2 -k + 1$

$\sf{}\Rightarrow k= 2 + 1$

$\sf{}\Rightarrow k= 3$

Therefore,value of k = 3

Answer 2

Note :-

The polynomial is wrong. The correct Polynomial is - 2x² + Kx + 1.

Given :-

x + 1 is factor of he polynomial 2x² + Kx + 1

To FinD :-

the value of k

Solution :-

x + 1 = 0

x = -1

Putting the value of x into the polynomial →

2x² + Kx + 1 = 0

2 × (-1)² + k × (-1) + 1 = 0

2 × 1 - k + 1 = 0

2 - k + 1 = 0

3 - k = 0

$\boxed{k = 3 }$