Question

If \(x^2+kx+1=0\) has a root x=1 then k=____

• A. 1
• B. 2
• C. 3
• D. -2

Answer 1

The Correct Option is D

To solve the problem, we need to determine the value of \( k \) such that the quadratic equation \( x^2 + kx + 1 = 0 \) has a root \( x = 1 \).

1. Substituting the Root into the Equation:
If \( x = 1 \) is a root of the equation, then substituting \( x = 1 \) into the equation should satisfy it. The given equation is:

\[ x^2 + kx + 1 = 0 \]

Substitute \( x = 1 \):

\[ (1)^2 + k(1) + 1 = 0 \]

This simplifies to:

\[ 1 + k + 1 = 0 \]

2. Solving for \( k \):
Combine like terms:

\[ 2 + k = 0 \]

Solve for \( k \):

\[ k = -2 \]

3. Verifying the Solution:
To ensure correctness, substitute \( k = -2 \) back into the original equation and check if \( x = 1 \) is indeed a root:

\[ x^2 - 2x + 1 = 0 \]

Factorize the quadratic equation:

\[ (x - 1)^2 = 0 \]

This confirms that \( x = 1 \) is a root.

Final Answer:
The value of \( k \) is \( {-2} \).