<p>The zeroes of the quadratic polynomial 16x<sup>2</sup> - 9 are:</p>
<p style="display:inline"><span class="math-tex">\(\frac{9}{16}\)</span>, <span class="math-tex">\(\frac{9}{16}\)</span></p>
<p style="display:inline"><span class="math-tex">\(-\frac{3}{4}\)</span>, <span class="math-tex">\(-\frac{3}{4}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{3}{4}\)</span>, <span class="math-tex">\(\frac{3}{4}\)</span></p>
<p style="display:inline"><span class="math-tex">\(-\frac{3}{4}\)</span>, <span class="math-tex">\(\frac{3}{4}\)</span></p>
Step-by-Step Solution
Key Concept: Identify the polynomial as a difference of squares and factorize it using the identity a^2 - b^2 = (a - b)(a + b) to find the zeroes.
<p>16x<sup>2</sup> - 9 = 0<br />
(4x - 3)(4x + 3) = 0<br />
<span class="math-tex">$\therefore$</span> x = <span class="math-tex">$\pm$</span><span class="math-tex">$\frac34$</span> </p>
Correct Answer: D