Question

For what value of k, does the quadratic equation 9x²+3x+4= 0, have equal roots?

• A. ±2
• B. ±3
• C. ±4
• D. ±9

Answer 1

The Correct Option is C

Step 1: Recall the condition for equal roots.

A quadratic equation \( ax^2 + bx + c = 0 \) has equal roots if its discriminant \( D = b^2 - 4ac \) is zero.

Step 2: Compute the discriminant.

Here, \( a = 9 \), \( b = 3k \), and \( c = 4 \). The discriminant is:

\[ D = (3k)^2 - 4(9)(4). \]

Simplify:

\[ D = 9k^2 - 144. \]

Step 3: Set the discriminant to zero and solve for \( k \).

\[ 9k^2 - 144 = 0 \implies 9k^2 = 144 \implies k^2 = 16 \implies k = \pm 4. \]

Final Answer: The value of \( k \) is \( \mathbf{\pm 4} \), which corresponds to option \( \mathbf{(3)} \).