The values of k for which the equation $4x^2 + kx + 9 = 0$ has real and equal roots are :

Step 1: Identify coefficients

First, we identify the coefficients $a$, $b$, and $c$ from the given quadratic equation $4x^2 + kx + 9 = 0$. Comparing it with the standard form of a quadratic equation, $ax^2 + bx + c = 0$, we find the values of $a$, $b$, and $c$.

Step 2: Apply condition for real and equal roots

For a quadratic equation to have real and equal roots, its discriminant ($D$) must be equal to zero. The discriminant is given by the formula $D = b^2 - 4ac$. We set this expression to zero.

Step 3: Substitute values and solve for k

Now, we substitute the identified values of $a=4$, $b=k$, and $c=9$ into the discriminant equation $b^2 - 4ac = 0$. This gives us an equation in terms of $k$, which we can then solve.

Step 4: Simplify and find k

We simplify the equation $k^2 - 144 = 0$ by adding 144 to both sides. Then, we take the square root of both sides to find the possible values of $k$. Remember that taking the square root yields both positive and negative solutions.

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