Question

If one root of the equation \( x^2 + kx - 6 = 0 \) is -2, then the value of \( k \) will be:

• A. 4
• B. 1
• C. -1
• D. 3

Hint:

To find the value of a parameter when one root of a quadratic equation is known, use Vieta’s formulas to relate the sum and product of the roots to the equation’s coefficients.

Answer 1

The Correct Option is C

Step 1: Use Vieta's formulas.
For the quadratic equation \( x^2 + kx - 6 = 0 \), Vieta's formulas give the relationships between the coefficients and the roots of the equation. The sum of the roots is \( -k \) and the product of the roots is \( -6 \). Let the roots be \( r_1 = -2 \) and \( r_2 \). The sum of the roots is: \[ r_1 + r_2 = -k \] Substituting \( r_1 = -2 \): \[ -2 + r_2 = -k \quad \Rightarrow \quad r_2 = -k + 2 \] The product of the roots is: \[ r_1 \times r_2 = -6 \] Substitute \( r_1 = -2 \) and solve for \( r_2 \): \[ -2 \times r_2 = -6 \quad \Rightarrow \quad r_2 = 3 \]
Step 2: Find \( k \).
Substitute \( r_2 = 3 \) into the sum of the roots equation: \[ -2 + 3 = -k \quad \Rightarrow \quad 1 = -k \quad \Rightarrow \quad k = -1 \]
Step 3: Conclusion.
Thus, the value of \( k \) is \( -1 \). Therefore, the correct answer is (C).