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 $\mathbf{(3)}$.