Question

If the roots of \(2x^2+kx+3=0\) are real and equal, then \(k=\)

• A. \(±6\sqrt 2\)
• B. ±4
• C. \(±2\sqrt 6\)
• D. ±5

Answer 1

The Correct Option is C

To solve this question, we need to determine the value of \( k \) when the roots of the quadratic equation are real and equal.

1. Given Equation:
The given quadratic equation is:
\[ 2x^2 + kx + 3 = 0 \]

2. Condition for Real and Equal Roots:
For the roots of a quadratic equation \( ax^2 + bx + c = 0 \) to be real and equal, the discriminant (\( \Delta \)) must be zero. The discriminant is given by:
\[ \Delta = b^2 - 4ac \]

3. Applying the Discriminant Formula:
In the given equation, \( a = 2 \), \( b = k \), and \( c = 3 \). The discriminant is:
\[ \Delta = k^2 - 4(2)(3) = k^2 - 24 \]

4. Setting the Discriminant to Zero:
For real and equal roots, the discriminant must be zero:
\[ k^2 - 24 = 0 \]

5. Solving for \( k \):
\[ k^2 = 24 \Rightarrow k = \pm \sqrt{24} = \pm 2\sqrt{6} \]

Final Answer:
Option (C) \( \pm 2\sqrt{6} \) is correct.