Question

If a quadratic equation \(2x^2 + kx+3=0\) have two equal roots then \(k=\)

• A. \(±6\sqrt 2\)
• B. \(±2\sqrt 2\)
• C. \(±2\sqrt 6\)
• D. \(±3\sqrt 2\)

Answer 1

The Correct Option is C

To solve the problem, we need to find the value of $k$ such that the quadratic equation $2x^2 + kx + 3 = 0$ has two equal roots.

1. Understanding the Condition for Equal Roots:
For a quadratic equation $ax^2 + bx + c = 0$ to have two equal roots, its discriminant must be zero.

Discriminant $D = b^2 - 4ac = 0$

2. Identifying Coefficients:
From the equation $2x^2 + kx + 3 = 0$, we have:
$a = 2$, $b = k$, $c = 3$

3. Applying the Discriminant Formula:
$k^2 - 4(2)(3) = 0$
$k^2 - 24 = 0$

4. Solving the Equation:
$k^2 = 24$
$k = \pm \sqrt{24} = \pm 2\sqrt{6}$

Final Answer:
The value of $k$ is $ \pm 2\sqrt{6} $.