Question

If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is

• A. 3
• B. –3
• C. –4
• D. \(\pm 3\)

Hint:

When taking the square root on both sides of an algebraic equation like \(k^2 = 9\), always remember to consider both the positive and negative roots.
A common error is to only write the positive value \(k = 3\), which would lead to selecting the incorrect option (A).
Always double-check all options before finalizing your answer!

Answer 1

The Correct Option is D

Step 1: Try writing the expression as a perfect square trinomial.
$9x^2=(3x)^2$ and $16=4^2$, so if $9x^2+8kx+16$ is a perfect square it should match $(3x\pm4)^2=9x^2\pm24x+16$.
Step 2: Match the middle term.
Comparing $8kx$ with $\pm24x$ gives $8k=\pm24$.
Step 3: Solve for $k$.
$k=\pm3$. A perfect square trinomial always has equal roots, so this directly gives the required values, matching option (D).
\[ \boxed{\pm3} \]